Inclusion Criteria:

1. Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study specific procedures.
2. Patients must have cytologically or histologically proven recurrent or metastatic squamous cell cancer of the head and neck (SCCHN) from the primary tumor or lymph nodes of the oral cavity, larynx, oropharynx, or hypopharynx.
3. No prior systemic chemotherapy for patients who present with metastatic disease. For patients with recurrent head and neck squamous cell carcinoma, prior chemotherapy is allowed if it was given as part of their definitive therapy. If patients have received prior combined modality therapy, they must be off therapy for at least 6 months.
4. Age >/= 18 years
5. Patients must have at least 1 evaluable lesion. Lesions must be evaluated by computed tomography (CT) scan or magnetic resonance imaging (MRI)
6. ECOG Performance Status (PS) of 0-1
7. Controlled blood pressure (defined as systolic BP </= 140 mmHg and diastolic </= 85 mmHg)
8. Adequate bone marrow, liver & renal function as assessed by the following laboratory requirements to be conducted w/in 7 days prior to start of first dose: Hemoglobin >/= 9.0 g/dL; Absolute neutrophil count (ANC) >/= 1,500/mm^3; Platelet count >/= 100,000/mm^3; Total bilirubin </= 1.5 times the upper limit of normal (ULN);ALT and AST </= 2.5 x ULN (</= 5 x ULN for pts w/ liver involvement); INR </= 1.5 and PTT w/in normal limits
9. Continued from Inclusion #8: Serum creatinine </= 1.5 ULN or creatinine clearance (CrCl) >/= 45 mL/min (CrCl = Wt (kg) x (140-age)/72 x Cr level, female x 0.85) for pts w/ creatinine levels above institutional normal; Amylase & lipase < 1.5 x the ULN; Urinalysis (UA) must show less than 1+ protein in urine, or the pt will require a repeat UA. If repeat UA shows 1+ protein or more, a 24 hour urine collection will be required & must show total protein </= 1000 mg/24 hour to be eligible
10. Women of childbearing potential (not surgically sterilized or at least 2 years postmenopausal) must have a negative serum or urine pregnancy test performed within 7 days prior to the start of treatment
11. Women of childbearing potential and men must agree to use adequate contraception (abstinence; hormonal or barrier method of birth control) prior to study entry, for the duration of study participation and 3 months after end of treatment. Should a woman become pregnant while participating or the partner of a patient participating in this study becomes pregnant, they should inform their treating physician immediately.

Exclusion Criteria:

1. Cardiac disease: Congestive heart failure (CHF) > Class II NYHA; active coronary artery disease (Myocardial infarction [MI] more than 6 months prior to study entry is allowed); or serious cardiac ventricular arrhythmias requiring anti-arrhythmic therapy (beta blockers or digoxin are permitted)
2. Uncontrolled hypertension defined as systolic blood pressure > 140 mmHg or diastolic pressure > 85 mmHg despite optimal medical management
3. Known history of Human Immunodeficiency Virus (HIV) infection or chronic hepatitis B or C
4. Active clinically serious infections (i.e. patients currently taking antibiotics)( Grade 2 NCI-CTC Version 3.0)
5. Evidence or history of central nervous system (CNS) disease, including primary brain tumors, seizures disorders, or any brain metastasis
6. Thrombotic or embolic events such as cerebrovascular accident, transient ischemic attacks, deep vein thrombosis or pulmonary embolism
7. Evidence or history of bleeding diathesis or coagulopathy
8. History of/or current evidence of hemoptysis (bright red blood of ½ teaspoon or more)
9. Peripheral neuropathy >/= Grade 2 (NCI-CTC Version 3.0)
10. Anticancer chemotherapy or immunotherapy: Anticancer therapy is defined as any agent or combination of agents with clinically proven anticancer activity administered by any route with the purpose of affecting the cancer, either directly or indirectly, including palliative and therapeutic endpoints
11. Radiotherapy to the target lesions within 3 weeks of start of first dose. Toxicities from radiotherapy must have resolved prior to start of first dose.
12. No major surgery, open biopsy or significant traumatic injury within 4 weeks of start of first dose
13. Serious, non-healing wound, ulcer, or bone fracture
14. Granulocyte growth factors (G-CSF), within 3 weeks of study entry.
15. Patients taking chronic erythropoietin are permitted provided no dose adjustment is made within 2 months prior to start of first dose.
16. Pregnant or breastfeeding patients
17. Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results
18. Known or suspected allergy to any recombinant human antibodies, or compounds of similar chemical or biologic composition to sorafenib or any of the drugs in this study
19. Any condition that is unstable or could jeopardize the safety or compliance of the patient in the study
20. Previous or concurrent cancer that is distinct in primary site or histology from the cancer being evaluated in the study EXCEPT cervical cancer in situ, treated basal cell carcinoma, superficial bladder tumors (Ta, Tis and T1) or any cancer curatively treated > 3 years prior to study entry
21. Any condition that impairs the patient's ability to swallow pills as a whole
22. Known or suspected allergy to sorafenib (BAY 43-9006) or any agent given in association with this trial
23. Any malabsorption conditions
24. Therapeutic anticoagulation with warfarin, heparins, or heparinoids
25. Patients taking phenytoin, carbamazepine, and Phenobarbital
26. Patients taking rifampin and/or St. John's Wort
27. Patients who are candidates for curative surgery or radiotherapy