Bevacizumab, Fluorouracil, and External-Beam Radiation Therapy in Treating Patients With Stage II or Stage III Rectal Cancer

Inclusion Criteria: * Histologically confirmed primary adenocarcinoma of the rectum that begins within 15 cm of the anal verge as determined by sigmoidoscopy and/or colonoscopy * Clinical T3 or T4 tumors as determined by the following features: * Tethered or fixed tumor on physical exam * cT3, cT4, or N+ disease must be confirmed by an endorectal ultrasound or surface coil MRI * There must be no evidence of metastatic disease as confirmed by physical examination, chest radiograph, and abdominal/pelvic CT scan * ECOG performance status 0, 1, 2 (Karnofsky \>= 70%) * Life expectancy of greater than 2 years * Leukocytes \>= 3,000/ul * Absolute neutrophil count \>= 1,500/ul * Platelets \>= 100,000/ul * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) \< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * The effects of bevacizumab on the developing human fetus are unknown; for this reason and because radiation therapy and 5-FU agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patients with no known HIV or HIV risk factors will be eligible for this study without HIV testing Exclusion Criteria: * Patients with a "concurrently active" second malignancy other than non- melanoma skin cancers or in situ cervical cancer are excluded; patients are not considered to have a "concurrently active" malignancy if they have completed therapy and considered by their physician to be at less than 30% risk of relapse at a minimum of 5 years after all therapy * Prior Treatment: * No prior treatment for this malignancy * No prior history of pelvic irradiation * No prior history of 5-FU-based therapy for any malignancy * No prior treatment with bevacizumab * Patients must not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition bevacizumab or other agents used in study * Bevacizumab - Specific exclusion criteria: * History or evidence upon physical examination of CNS disease (e.g., primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases, or history of stroke * Serious, non-healing wound, ulcer, or bone fracture * Clinically significant cardiovascular disease (e.g., uncontrolled hypertension, history of myocardial infarction, unstable angina within 12 months), New York Heart Association (NYHA) Grade II or greater congestive heart failure, serious cardiac arrhythmia requiring medication, or Grade II or greater peripheral vascular disease within 1 year prior to Day 0 * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 0, or anticipation of need for major surgical procedure during the course of the study; biopsies (other than rectal cancer) within 7 days prior to Day 0; placement of a vascular access device within 7 days prior to Day 0 * Arterial thromboembolic events within previous 12 months including transient ischemic attack, cerebrovascular accident, unstable angina, myocardial infarction, or clinically significant peripheral vascular disease. Vascular surgery, stenting or angioplasty within previous 12 months; no history of venous thromboembolic events that require continuation of therapeutic dose of anticoagulation * Current or recent (within 10 days prior to Day 0) use of full-dose oral or parenteral anticoagulants or thrombolytic agents (except as required to maintain patency of preexisting, permanent indwelling IV catheters; for subjects receiving warfarin, international normalized ratio \[INR\] of \< 1.5; appropriate use of heparin should be discussed with the Medical Monitor) * Chronic, daily treatment with aspirin (\> 325 mg/day) or nonsteroidal anti- inflammatory medications (of the kind known to inhibit platelet function at doses used to treat chronic inflammatory diseases) * Presence of bleeding diathesis or coagulopathy * Active infection requiring parenteral antibiotics on Day 0 * Proteinuria at baseline or clinically significant impairment of renal function * Subjects unexpectedly discovered to have \>= 1+ proteinuria during screening should undergo a 24-hour urine collection, which must be an adequate collection and must demonstrate \< 1 gram protein/24 hr to allow participation in the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because bevacizumab, radiation therapy, and 5-FU have potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with bevacizumab, breastfeeding should be discontinued if the mother is treated with bevacizumab; these potential risks may also apply to other agents used in this study