Inclusion Criteria:

- Patients must have histopathologically confirmed at MSKCC thyroid carcinoma.

- Patient must agree to allow 2 biopsies of any malignant lesion that can be accessed
by ultrasound (e.g., cervical lymph node, peripheral nodule) or without the aid of
radiology (i.e., skin lesion)

- Patients must have surgically inoperable and/or recurrent/metastatic disease.

- Patients must have a PET scan prior to the protocol start date and have at least one
FDG-avid lesion that has not been removed surgically or radiated (unless it has
progressed by RECIST criteria after the completion of radiation therapy and is still
FDG-avid). FDG-avidity will be defined as any focus of increased FDG uptake greater
than normal activity with SUV maximum levels greater than or equal to 3. PET scan can
have been done at any time prior to the start of therapy, although it is recommended
that it be done within 3 months prior to the start of therapy.

- Patients must have measurable disease by RECIST criteria, defined as at least one
lesion that can be accurately measured in at least one dimension (longest diameter to
be recorded) as ≥ 20 mm with conventional techniques or as ≥ 10 mm with spiral CT
scan; performed ≤ 4 weeks of protocol start date.

- Patients must have progressive disease defined by at least one of the following
occurring during or after previous treatment (including RAI treatment) unless newly
diagnosed:

- The presence of new or progressive lesions on CT/MRI.

- New lesions on bone scan or PET scan.

- Rising thyroglobulin level (documented by a minimum of three consecutive rises, with
an interval of > 1 week between each determination).

- Prior RAI therapy is allowed if > 3 months prior to initiation of therapy on this
protocol and evidence of progression (as defined above) has been documented in the
interim. A diagnostic study using <10 mCi of RAI is not considered RAI therapy.

- Patients may have received prior external beam radiation therapy to index lesions ≥ 4
weeks prior to initiation of therapy on this protocol if there has been documented
progression by RECIST criteria. Prior external beam radiation therapy to the
non-index lesions is allowed if ≥ 4 weeks prior to initiation of therapy on this
protocol.

- ECOG performance status ≤ 2 (or Karnofsky performance status ≥ 60%).

- Patients must have normal organ and marrow function as defined below:

- Absolute neutrophil count ≥1,500/mcL

- Hemoglobin > 9 gm/dl

- Platelets ≥100,000/mcL

- Total bilirubin ≤ 1.5 X institutional ULN (unless increase is due to indirect
bilirubin only such as Gilbert's disease)

- AST(SGOT)/ALT(SGPT) ≤ 2.5 X institutional ULN unless liver metastasis present. or
AST(SGOT)/ALT(SGPT) ≤ 5 X institutional ULN if liver metastasis is present.

- Creatinine ≤ 1.5 X institutional ULN OR Creatinine clearance ≥ 60 mL/min/1.73 m2 for
patients with creatinine levels above 1.5 X institutional ULN [in this circumstance,
either of a measured level based on a 24 hour urine collection, or a calculated level
using the Cockcroft and Gault equation: (140 - age in years) X (weight in kg) X (0.85
if female)/72 X serum Cr may be used].

- International normalized ratio (INR) ≤ 1.5 (or in range INR, usually between 2 and
3, if patient is on a stable dose of therapeutic warfarin).

ULN = upper limit of normal

- Fasting serum cholesterol ≤300 mg/dL OR ≤7.75 mmol/L AND fasting triglycerides ≤ 2.5
x ULN. NOTE: In case one or both of these thresholds are exceeded, the patient can
only be included after initiation of appropriate lipid lowering medication.

- Ability to understand and the willingness to sign a written informed consent
document.

- Age 18 years old or older.

Exclusion Criteria:

- Anaplastic thyroid carcinoma present in any biopsy or fine needle aspirate specimen
over the previous year, unless a pathologist at MSKCC disagrees with this diagnosis.

- Previous treatment with a known mTOR inhibitor (e.g., everolimus, temsirolimus) or
sorafenib for thyroid cancer.

- Patients currently receiving anticancer therapies or who have received anticancer
therapies within 4 weeks of the start of study drug (including chemotherapy,
radiation therapy, antibody based therapy, etc.)

- Patients, who have had a major surgery or significant traumatic injury within 4 weeks
of start of study drug, patients who have not recovered from the side effects of any
major surgery (defined as requiring general anesthesia) or patients that may require
major surgery during the course of the study

- Patients receiving chronic, systemic treatment with corticosteroids or another
immunosuppressive agent. Topical or inhaled corticosteroids are allowed.

- Patients should not receive immunization with attenuated live vaccines within one
week of study entry or during study period

- Patients may not be receiving any other investigational agents.

- Patients with known history of active intraparenchymal brain metastasis within
previous 3 months. Previously treated lesions are eligible if they either have been
surgically removed and there are no indications of metastatic disease on imaging of
the brain or if there has been no progression after treatment for at least 6 months.

- Serious or non-healing wound, ulcer, or bone fracture.

- History of abdominal fistula, gastrointestinal perforation, or intra-abdominal
abscess within 28 days of treatment.

- Impairment of gastrointestinal function or gastrointestinal disease that may
significantly alter the absorption of RAD001 or sorafenib (e.g., ulcerative disease,
uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel
resection)

- Patients with clinically significant cardiovascular disease as defined by the
following:

- History of CVA within past 6 months

- Myocardial infarction, CABG or unstable angina within past 6 months

- New York Heart Association grade III or greater congestive heart failure or Canadian
Cardiovascular Class grade III or greater angina within past 6 months (Appendices
A&B)

- Clinically significant peripheral vascular disease within past 6 months

- Pulmonary embolism, DVT, or other thromboembolic event within past 6 months

- Uncontrolled coronary artery disease, angina, congestive heart failure, or
ventricular arrhythmia requiring acute medical management within past 6 months

- History of myocardial infarct, cerebrovascular accident, or transient ischemic event
within the past 6 months

- liver disease such as cirrhosis, chronic active hepatitis or chronic persistent
hepatitis

- active (acute or chronic) or uncontrolled severe infections

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection or psychiatric illness/social situations that would limit compliance with
study requirements.

- While the use of Angiotensin-Converting Enzyme (ACE) inhibitors is not absolutely
excluded, efforts should be made to see if patients on ACE inhibitors can be taken
off the medication or switched to another medication.

- Patients with an active, bleeding diathesis

- Female patients who are pregnant or breast feeding, or adults of reproductive
potential who are not using effective birth control methods. If barrier
contraceptives are being used, these must be continued throughout the trial by both
sexes. Hormonal contraceptives are not acceptable as a sole method of contraception.
(Women of childbearing potential must have a negative serum pregnancy test within 14
days prior to administration of RAD001)

- Patients with a known hypersensitivity to RAD001 (everolimus) or other rapamycins
(sirolimus, temsirolimus) or to its excipients.

- History of noncompliance to medical regimens

- Patients unwilling to or unable to comply with the protocol

- A known history of HIV seropositivity

- The use of agents that inhibit or induce CYP3A metabolism is not strictly prohibited,
but should be avoided if possible. Potential CYP3A inducing agents include
carbamazepine, phenytoin, barbiturates, rifabutin, rifampicin, and St. John's Wort.
Potential CYP3A inhibitors include protease inhibitors, antifungals, macrolide
antibiotics, nefazodone, and selective serotonin inhibitors.