Stereotactic Body Radiation Therapy and Aflibercept in Treating Patients With Uveal Melanoma

Inclusion Criteria: * Provide signed and dated informed consent form or have a Legally Authorized Representative (LAR) who can give consent * Willing to comply with all study procedures and be available for the duration of the study * Must be a candidate for radiation therapy * Karnofsky performance status (KPS) \>= 60 * Diagnosed with uveal melanoma either clinically or pathologically on biopsy * Uveal melanoma of one eye only * Localized uveal melanoma, with no evidence of metastasis * Women of childbearing potential must have a negative urine or serum pregnancy test within 14 days prior to enrollment Exclusion Criteria: * Tumor thickness more than 14 mm as measured by ultrasound * Active collagen vascular disease * Any contraindication to intravitreal injections including: elevated intraocular pressure, ocular or periocular infection, active intraocular inflammation, or other determined by treating physician * Known allergic reactions to components of intravitreal Aflibercept * Patients with known hypercoagulable syndromes * Prior radiation to the eye or brain * Life expectancy less than 6 months * Blind in both eyes * Patients unable to receive contrast enhanced brain magnetic resonance imaging (MRI) * Deaf in both ears * Patients have hypersensitivity to intravitreal Aflibercept * Patients is on or within 1 month of systemic anti-VEGF treatment * Patients who are candidates for brachytherapy * Patients for whom enucleation is standard of care * Pregnancy or active breastfeeding. Sexually active men or women of childbearing potential who are unwilling to practice adequate contraception prior to the initial dose/start of the first treatment, during the study, and for at least 3 months after the last dose. Adequate contraceptive measures include stable use of oral contraceptives or other prescription pharmaceutical contraceptives for 2 or more menstrual cycles prior to screening; intrauterine device; bilateral tubal ligation; vasectomy; condom plus contraceptive sponge, foam, or jelly, or diaphragm plus contraceptive sponge, foam, or jelly * Contraception is not required for men with documented vasectomy * Postmenopausal women must be amenorrheic for at least 12 months in order not to be considered of childbearing potential. Pregnancy testing and contraception are not required for women with documented hysterectomy or tubal ligation