DISEASE CHARACTERISTICS:

• Histologically confirmed diagnosis of 1 of the following:

  • Papillary thyroid cancer (stratum I)

  • Papillary, follicular, Hurthle cell, insular, or anaplastic thyroid cancer (stratum II)

    • Mixed histology, poorly differentiated, or tall-cell variants allowed
• Metastatic, locally advanced, or locally recurrent disease

• At least 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan

  • The following are considered non-measurable disease:

    • Tumors in a previously irradiated area
    • Bone lesions
    • Leptomeningeal disease
    • Ascites
    • Pleural/pericardial effusion
    • Lymphangitis cutis/pulmonis
    • Abdominal masses not confirmed and followed by imaging techniques
    • Cystic lesions
• Archival tumor tissue block OR material collected before study entry available (stratum I)
• Biopsy-accessible disease (stratum I)

PATIENT CHARACTERISTICS:

Age

• 18 and over

Performance status

• ECOG 0-1

Life expectancy

• At least 6 months

Hematopoietic

• WBC ≥ 3,000/mm^3
• Absolute neutrophil count ≥ 1,500/mm^3
• Platelet count ≥ 100,000/mm^3
• No bleeding diathesis

Hepatic

• Bilirubin ≤ 1.5 times upper limit of normal (ULN)
• AST and ALT ≤ 1.5 times ULN

Renal

• Creatinine ≤ 1.5 times ULN

Cardiovascular

• No uncontrolled hypertension

Other

• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception
• Willing to undergo 2 tumor biopsies during study participation (stratum I)
• No history of allergic reaction attributed to compounds of similar chemical or biologic composition to sorafenib
• No ongoing or active infection
• No psychiatric illness or social situation that would preclude study compliance
• No other uncontrolled illness
• No other concurrent malignancy except nonmetastatic nonmelanoma skin cancer or carcinoma in situ of the cervix

PRIOR CONCURRENT THERAPY:

Biologic therapy

• Not specified

Chemotherapy

• No prior systemic chemotherapy for thyroid cancer (stratum I)

  • Prior systemic chemotherapy used to treat a second primary cancer with curative intent allowed provided the primary cancer was treated more than 5 years before study entry
• No more than 3 prior systemic chemotherapy regimens for thyroid cancer (stratum II)
• More than 6 weeks since prior systemic chemotherapy (stratum II)

Endocrine therapy

• Not specified

Radiotherapy

• See Disease Characteristics
• No prior external beam radiotherapy to the sole site of measurable disease (except for patients with anaplastic thyroid cancer)
• More than 6 weeks since prior external beam radiotherapy
• More than 24 weeks since prior iodine I 131

Surgery

• Not specified

Other

• Recovered from all prior therapy
• No prior sorafenib
• More than 6 weeks since prior investigational tumor-specific therapy
• Concurrent oral or IV bisphosphonates for bony metastases allowed at the discretion of the investigator
• No other concurrent tumor-specific or investigational therapy
• No concurrent combination antiretroviral therapy for HIV-positive patients

• No concurrent therapeutic anticoagulation

  • Concurrent prophylactic anticoagulation (e.g., low-dose warfarin) for venous or arterial access devices allowed provided PT, INR, or PTT are normal