Inclusion Criteria:

- Patients must have a diagnosis of HCC by at least one criterion listed below:

- Pathologically (histologically or cytologically) proven diagnosis of HCC, within
180 days of study entry; (biopsies are recommended, and are to be submitted for
research evaluation if patients consent)

- At least one solid liver lesion or vascular tumor thrombosis (involving portal
vein, inferior vena cava [IVC] and/or hepatic vein) > 1 cm demonstrating early
arterial enhancement and delayed washout on multi-phasic computerized tomography
(CT) or magnetic resonance imaging (MRI) in the setting of cirrhosis or chronic
hepatitis B or C without cirrhosis, within 180 days of study entry; note,
patients with vascular thrombosis as the only manifestation of HCC are eligible,
if they meet other eligibility criteria

- Measureable hepatic disease and/or presence of vascular tumor thrombosis (involving
portal vein, IVC and/or hepatic vein) which may not be measureable as per Response
Evaluation Criteria in Solid Tumors (RECIST) on liver CT or MRI, within 28 days of
registration

- Appropriate for protocol entry based upon the following minimum diagnostic workup:

- History/physical examination including examination for encephalopathy, ascites,
weight, height, and blood pressure within 14 days prior to study entry

- Assessment by radiation oncologist and medical oncologist or hepatologist who
specializes in treatment of HCC within 28 days prior to study entry

- Pre-randomization Scan (REQUIRED for All Patients): CT scan chest/abdomen/pelvis
with multiphasic liver CT scan within 28 days prior to study entry; if CT
contrast is contraindicated, CT chest without contrast and MRI of abdomen and
pelvis is permitted

- Zubrod performance status 0-2 within 28 days prior to study entry

- Absolute neutrophil count (ANC) >= 1,500 cells/mm^3

- Platelets >= 70,000 cells/mm^3

- Hemoglobin >= 8.0 g/dl (note: the use of transfusion or other intervention to achieve
hemoglobin [Hgb] >= 8.0 g/dl is acceptable)

- Total bilirubin < 2 mg/dL

- Prothrombin time/international normalized ratio (INR) < 1.7

- Albumin >= 28 g/L

- Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) < 6 times upper
limit of normal (ULN)

- Serum creatinine =< 1.5 x ULN or creatinine clearance >= 60 mL/min

- Barcelona Clinic Liver Cancer (BCLC) stage: intermediate (B) or advanced (C) within
14 days prior to study entry

- Child-Pugh score A within 14 days prior to study entry

- Women of childbearing potential and male participants must agree to practice adequate
contraception while on study and for at least 6 months following the last dose of
radiation therapy (RT) and for at least 28 days following the last dose of sorafenib
(whichever is later)

- Unsuitable for resection or transplant or radiofrequency ablation (RFA)

- Unsuitable for or refractory to transarterial hepatic chemo-embolization (TACE) or
drug eluting beads (DEB) for any of the following reasons, as described by Raoul et
al (2011):

- Technical contraindications: arteriovenous fistula, including transjugular
intrahepatic portosystemic shunt (TIPS), surgical portosystemic shunt,
spontaneous portosystemic shunt or hepatofugal portal vein flow

- Severe reduction in portal vein flow: due to tumor portal vein, IVC or atrial
invasion or bland portal vein occlusion

- Medical contraindications including congestive heart failure, angina, severe
peripheral vascular disease

- Presence of extrahepatic disease

- No response post TACE (or DEB) x 2 or progressive HCC despite TACE; prior TACE
or DEB is allowed but must be > 28 days from study entry

- Serious toxicity following prior TACE (or DEB); prior TACE or DEB must be > 28
days from study entry

- Other medical comorbidities making TACE (or DEB) unsafe and/or risky (e.g.
combination of relative contraindications including age > 80 years, tumor > 10
cm, > 50% replacement of the liver by HCC, extensive multinodular bilobar HCC,
biliary drainage)

- Patients treated with prior surgery are eligible for this study if they otherwise
meet eligibility criteria

- Patient must be able to provide study-specific informed consent prior to study entry

Exclusion Criteria:

- Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free
for a minimum of 2 years (note that carcinoma in situ of the breast, oral cavity, or
cervix are all permissible)

- Prior sorafenib use; note that prior chemotherapy for HCC or a different cancer is
allowable

- Prior radiotherapy to the region of the liver that would result in overlap of
radiation therapy fields

- Prior selective internal radiotherapy/hepatic arterial yttrium therapy, at any time

- Severe, active co-morbidity, defined as follows:

- Unstable angina and/or congestive heart failure requiring hospitalization within
the last 6 months before registration

- Transmural myocardial infarction within the last 6 months prior to study entry

- Unstable ventricular arrhythmia within the last 6 months prior to study entry

- Acute bacterial or fungal infection requiring intravenous antibiotics within 28
days prior to study entry

- Hepatic insufficiency resulting in clinical jaundice, encephalopathy and/or
variceal bleed within 60 days prior to study entry

- Bleeding within 60 days prior to study entry due to any cause, requiring
transfusion

- Thrombolytic therapy within 28 days prior to study entry. Subcutaneous heparin
is permitted.

- Known bleeding or clotting disorder

- Uncontrolled psychotic disorder

- Pregnancy or women of childbearing potential and men who are sexually active and not
willing/able to use medically acceptable forms of contraception; this exclusion is
necessary because the treatment involved in this study may be significantly
teratogenic

- Any one hepatocellular carcinoma > 15 cm

- Total maximal sum of hepatocellular carcinoma > 20 cm

- More than 5 discrete intrahepatic parenchymal foci of HCC

- Direct tumor extension into the stomach, duodenum, small bowel or large bowel

- Measureable common or main branch biliary duct involvement with HCC

- Extrahepatic metastases or malignant nodes (that enhance with typical features of
HCC) > 2.0 cm, in sum of maximal diameters (e.g. presence of one 2.4 cm metastatic
lymph node or two 1.2 cm lung lesions); note that benign non-enhancing periportal
lymphadenopathy is not unusual in the presence of hepatitis and is permitted, even if
the sum of enlarged nodes is > 2.0 cm

- Use of regular phenytoin, carbamazepine, hypericum perforatum (also known as St.
John's wort) or rifampin

- Use of combination anti-retroviral therapy for human immunodeficiency virus (HIV), as
these agents may modulate cytochrome P450 isozymes