Inclusion Criteria:

1. Patients with advanced solid tumor malignancy for whom no effective therapy exists or who have failed effective therapy. Exceptions are patients with advanced solid malignancies where either capecitabine or sorafenib has been approved as initial chemotherapy either alone or in combination.
2. A maximum of 4 prior cytotoxic chemotherapy regimens in the metastatic setting.
3. Patients previously treated with capecitabine or infusional 5-FU are eligible, but must not have been a part of the immediately prior regimen, or received the treatment within 3 months prior to study initiation.
4. Patients who have received prior radiation therapy are eligible, provided that this is not the only site of evaluable disease. Prior therapy must have been completed > 3 weeks before study enrollment.
5. An Eastern Cooperative Oncology Group performance status (ECOG PS) of 0-1.
6. Life expectancy of > 3 months.

7. Adequate bone marrow, liver, and renal function as assessed by the following:

   • Hemoglobin ≥ 9.0 g/dL
   • Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 × upper limit of normal range (ULN) (unless liver metastases are present, then ≤ 5 × ULN is allowed)
   • Total bilirubin ≤ 1.5 x ULN
   • Serum creatinine ≤ 1.5 x ULN
   • ANC ≥ 1.5 × 109/L
   • Platelets ≥ 100 × 109/L
   • International Normalized Ratio for prothrombin time (PT-INR) ≤ 1.5 and activated partial thromboplastin time (aPTT) within normal limits
8. Patients must be able to swallow and retain oral medications.
9. Resolution of all acute toxic effects of prior chemotherapy, radiotherapy, or surgical procedure to grade ≤ 1 per the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE).
10. Patients with a history of brain metastasis treated with radiation and/or surgery ≥ 8 weeks prior to study enrollment are eligible for the study if the effects of that treatment have resolved. These patients must have a post-treatment magnetic resonance imaging (MRI) of the brain within 8 weeks of study entry that shows no new brain metastasis and no further progression of prior lesions.
11. Patients with deep vein thrombosis/pulmonary embolism (DVT/PE) are allowed if they have been on anti-coagulation for > 3 months, and they are on a stable dose of coumadin with 2 serial documented individual normalized ratios (INRs) in the therapeutic range at least 72 hours apart.
12. Women of childbearing potential and men with partners of childbearing potential must agree to use a method of contraception that is acceptable to their physicians from time of first signing the informed consent until at least 12 weeks after the end of study drug administration. If a woman becomes pregnant or suspects she is pregnant while participating in this study, she must agree to inform her treating physician immediately.
13. Ability to understand and willingness to sign a written informed consent document.
14. Willingness and ability to comply with scheduled visits, treatment arrangements, laboratory tests, and other study procedures.

Exclusion Criteria:

1. Known untreated brain metastasis.
2. Prior irradiation to > 25% of the bone marrow (whole pelvis = 25%).
3. Any previous major surgery within 4 weeks of the start of the study, or within 1 week of any minor surgical procedure (e.g., dental work, port placement, etc.).
4. Treatment with chemotherapy or an investigational new drug within 28 days of day 1 of treatment.
5. No prior anti-vascular endothelial growth factor (VEGF) therapy (with the exception of bevacizumab if the last dose was > 3 months prior to study treatment), including VEGF receptor inhibitors, thalidomide or thalidomide-like therapy, or any other (including investigational) anti-angiogenic treatment of any kind. Only prior bevacizumab is allowed.
6. Patients with any serious medical risk factors involving any of the major organ systems such that the investigator considers it unsafe for the patient to receive an experimental research drug.
7. Evidence or history of bleeding diathesis or coagulopathy.
8. Any serious non-healing wound, ulcer, or bone fracture.
9. Cardiac disease, including: congestive heart failure (CHF) > Class II per New York Heart Association (NYHA) classification (see Appendix B); unstable angina (anginal symptoms at rest) or new-onset angina (i.e., began within the last 3 months), or myocardial infarction within the past 6 months; symptomatic CHF, unstable angina pectoris, cardiac arrhythmia, or cardiac ventricular arrhythmias requiring anti-arrhythmic therapy.
10. Uncontrolled hypertension (i.e., systolic blood pressure > 150 mm Hg or diastolic pressure > 90 mm Hg despite optimal medical management).
11. Psychiatric illness/social situations that would limit compliance with study requirements.
12. Patients with active, uncontrolled bacterial, viral, or fungal infection(s) requiring systemic therapy.
13. Patients with a history of DVT/PE are not allowed if the thrombosis occurred within the last 6 months.
14. Pulmonary hemorrhage or bleeding event > grade 2 within 4 weeks of study randomization.
15. Any other hemorrhage/bleeding event ≥ grade 3 within 4 weeks of study randomization.
16. Known human immunodeficiency virus (HIV) infection or chronic hepatitis B or C.
17. Known or suspected allergy to sorafenib, or hypersensitivity to capecitabine or any of the components of fluorouracil.
18. History of severe and unexpected reactions to fluoropyrimidine therapy, or patients with dihydropyrimidine dehydrogenase deficiency.
19. Concomitant use of St. John's Wort or rifampin (rifampicin).
20. Women who are pregnant or breastfeeding.
21. Any condition that impairs patient's ability to swallow whole pills.
22. Patients with gastrointestinal (GI) tract disease, causing the inability to take oral medication, malabsorption syndrome, a requirement for intravenous (IV) alimentation, prior surgical procedures affecting absorption, uncontrolled inflammatory GI disease (e.g., Crohn's Disease, ulcerative colitis).