Neoadjuvant Celecoxib and Capecitabine Combined With Pelvic Irradiation in Treating Patients With Stage II or Stage III Adenocarcinoma (Cancer) of the Rectum

DISEASE CHARACTERISTICS: * Histologically confirmed rectal adenocarcinoma * Clinical stage T3, N0, M0 OR any T, N1-3, M0 disease * Treatment with neoadjuvant chemotherapy and pelvic radiotherapy is indicated * All disease must be encompassable within standard pelvic radiotherapy fields * Distal border of the tumor must be at or below\* the peritoneal reflection, defined as within 12 cm of the anal verge by endoscopy NOTE: \*If a portion of the tumor is below the peritoneal reflection at the time of surgery, patients are eligible regardless of the distance of the tumor determined at endoscopy * Tumor must be determined to be clinically resectable * Tumor may not be clinically fixed * Negative margins by routine examination of an unanesthetized patient * Transmural penetration of tumor through the muscularis propria by CT scan, endorectal ultrasound, or MRI * No distant metastatic disease * No evidence of tumor outside the pelvis, including any of the following: * Metastatic inguinal lymphadenopathy * Peritoneal seeding * Liver metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-1 Life expectancy * At least 6 months Hematopoietic * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 Hepatic * Bilirubin ≤ upper limit of normal (ULN) * AST ≤ 3 times ULN * Alkaline phosphatase ≤ 4 times ULN if AST \< ULN Renal * Creatinine clearance ≥ 30 mL/min * No renal impairment Cardiovascular * No congestive heart failure * No symptomatic coronary artery disease * No uncontrolled cardiac arrhythmias * No myocardial infarction * No history of transient ischemic attacks or stroke * No other clinically significant cardiac disease Gastrointestinal * No bleeding peptic ulcer disease within the past 12 months * No lack of physical integrity of the upper gastrointestinal tract * No malabsorption syndrome * No active inflammatory bowel disease * Must be able to swallow study drugs Other * No dihydropyrimidine dehydrogenase deficiency * No history of uncontrolled seizures * No CNS disorders * No clinically significant psychiatric illness that would preclude study compliance or giving informed consent * No other malignancy within the past 5 years except basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * No known sensitivity to NSAIDs, sulfonamides, or aspirin * No other serious medical illness that would preclude study treatment * No other conditions that would preclude study participation * Must be able to tolerate major surgery that may include abdominal-perineal resection * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 30 days after study treatment PRIOR CONCURRENT THERAPY: Biologic therapy * Not specified Chemotherapy * See Disease Characteristics * No prior systemic anticancer chemotherapy Endocrine therapy * Not specified Radiotherapy * See Disease Characteristics * No prior radiotherapy to the pelvis Surgery * See Disease Characteristics * More than 3 weeks since prior major surgery and recovered Other * At least 7 days since prior nonsteroidal anti-inflammatory drugs (NSAIDs), including aspirin * No other concurrent investigational drugs * No other concurrent anticancer treatment * No concurrent NSAIDs * No concurrent primary prophylactic therapy for hand-foot syndrome * No concurrent loperamide prophylaxis for diarrhea * No concurrent sorivudine or brivudine