Since thyroid cancer becomes refractory to radioactive iodine, treatment options are very limited. Tyrosine kinase inhibitors such as sorafenib have recently shown promise. This trial seeks to expand treatment options for this disease with a new, oral drug called RAD001. It is an inhibitor of the mTOR pathway and has shown activity in neuroendocrine cancers of the gastrointestinal tract and has been approved for the treatment of metastatic renal cell cancer.

• RAD001 will be taken once a day in the morning starting on Day 1 and continue until the participant is no longer participating in the study treatment.
• A history and physical exam will be performed the first day of the study and then once a month. Blood tests including coagulation studies, and thyroid studies will be performed monthly. A urine sample will need to be provided on the first day of treatment and then every 2 months. Imaging consisting of a CT or MRI of the neck, chest and abdomen will be done every 8 weeks after starting RAD001.
• Participants will remain on this research study for up to 24 months. However, if the participants doctor feels that they are benefiting from the study drug and they do not have severe side effects, they may be given the option to continue taking RAD001.

Inclusion Criteria:

• Histologically confirmed locally advanced or metastatic thyroid cancer, excluding thyroid lymphomas not amenable to or refractory to surgical resection, external beam radiotherapy, radioiodine or other local therapies.
• Prior therapy with chemotherapy and targeted therapies except for mTor inhibitors is allowed.
• Medullary thyroid cancer with documented evidence of disease progression by modified RECIST within 6 months before study day 1 or symptomatic disease at the time of screening in the absence of documented disease progression.
• Differentiated thyroid cancer with documented evidence of disease progression by modified RECIST within 6 months before study day 1.
• Anaplastic thyroid cancer with disease progression with documented disease progression by modified RECIST within 6 months of study day 1.
• Patients must have at least one measurable site of disease according to RECIST criteria that has not previously irradiated. If the patient has has previous radiation to the marker lesion(s), there must be evidence of progression since radiation.
• 18 years of age or older
• WHO performance status 2 or less
• Adequate bone marrow, liver, and renal function
• Fasting serum cholesterol 300mg/dL or less OR 7.75 mmol/L or less AND fasting triglycerides 2.5x ULN or less

Exclusion Criteria:

• Patients receiving anticancer therapies within last 2 weeks or who have received radiation therapy within 3 weeks of study day 1
• Prior therapy with mTOR inhibitors
• 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 or patients that may require major surgery during the course of the study
• Prior treatment with any investigational drug within the preceding 3 weeks
• 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 2 weeks of study entry or during study period
• Uncontrolled brain or leptomeningeal metastases, including patients who continue to require glucocorticoids for brain or leptomeningeal metastases
• Other malignancies within the past 3 years except for adequately treated carcinoma of the cervix or basal or squamous cell carcinomas of the skin
• Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study
• A known history of HIV seropositivity
• Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001
• 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
• Patients who have received prior treatment wih an mTOR inhibitor
• Patients with a known hypersensitivity to RAD001 or other rapamycins or to its excipients
• History of noncompliance to medical regimens

Assessed while on treatment and then up to 30 days after discontinuing treatment; up to 31 months