This phase II trial studies how well giving bevacizumab, radiation therapy, and combination chemotherapy works in treating patients who are undergoing surgery for locally advanced nonmetastatic rectal cancer. Monoclonal antibodies, such as bevacizumab, can block tumor growth in different ways. Some find tumor cells and kill them or carry tumor-killing substances to them. Others interfere with the ability of tumor cells to grow and spread. Bevacizumab may also stop the growth of tumor cells by blocking blood flow to the tumor. Radiation therapy uses high-energy x-rays to kill tumor cells. Drugs, such as capecitabine, may make tumor cells more sensitive to radiation therapy. Drugs used in chemotherapy, such as capecitabine, oxaliplatin, fluorouracil, and leucovorin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving bevacizumab together with radiation therapy and combination chemotherapy before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. Giving bevacizumab together with combination chemotherapy after surgery may kill any tumor cells that remain after surgery.