A Trial of ZD6474, Paclitaxel, Carboplatin, 5-Fluorouracil, and Radiation Therapy Followed by Surgery

Inclusion criteria: * Histologically documented carcinoma of the esophagus, gastroesophageal junction, or stomach for which chemo/radiation therapy is appropriate. * Potentially resectable esophageal, Gastroesophageal junction carcinoma, or stomach carcinoma * Eastern Cooperative Oncology Group Performance Status = 0-2 * No evidence of distant metastases * Age 18 or greater * Signed informed consent * Willingness to practice adequate contraception in women of childbearing potential (WOCBP). Contraception must be continued for one month following discontinuation of the study drugs. Females who are WOCBP must have negative pregnancy test within 7 days of the first treatment. WOCBP includes any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or is postmenopausal (defined as amenorrhea \>=12 consecutive months, or women on hormone replacement therapy (HRT) with documented plasma follicle-stimulating hormone (FSH) level \>35 mIU/mL). Even women who are using oral, implanted, or injectable contraceptive hormones or mechanical products (diaphragm, condoms, spermicides) to prevent pregnancy or practicing abstinence or where partner is sterile (e.g. vasectomy), should be considered to be WOCBP. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. Exclusion criteria: * Previous radiation therapy to chest or upper abdomen. * Evidence of severe or uncontrolled systemic disease or any concurrent condition which in the Investigator's opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol. * Impaired cardiac function at baseline, including any of the following: * Clinically significant cardiac event such as myocardial infarction; New York Heart Association (NYHA) classification of heart disease \>2 within 3 months before registration; or presence of cardiac disease that, in the opinion of the Investigator, increases the risk of ventricular arrhythmia. * Inadequate pulmonary and cardiac function to tolerate surgery (see section 12): left ventricular ejection fraction \<45% and/or a positive stress test; or Forced Expiratory Volume (FEV1) of \<1.1 liters. * History of arrhythmia (multifocal premature ventricular contractions (PVCs), bigeminy, trigeminy, ventricular tachycardia, or uncontrolled atrial fibrillation) which is symptomatic or requires treatment or asymptomatic sustained ventricular tachycardia. Atrial fibrillation, controlled on medication is not excluded. * Previous history of QTc prolongation as a result from other medication that required discontinuation of that medication. * Congenital long QT syndrome, or 1st degree relative with unexplained sudden death under 40 years of age. * Presence of left bundle branch block (LBBB). * QTc with Bazett's correction that is unmeasurable, or \>or= 480 msec on screening ECG. If a patient has QTc \>or= 480 msec on screening ECG, the screen ECG may be repeated twice (at least 24 hours apart). The average QTc from the three screening ECGs must be \<480 msec in order for the patient to be eligible for the study). * Any concomitant medication that may cause QTc prolongation, induce Torsades de Pointes or induce CYP3A4 function * Hypertension not controlled by medical therapy (systolic blood pressure greater than 160 mm Hg or diastolic blood pressure greater than 100 mm Hg) * Women who are currently pregnant or breast feeding. * Previous or current malignancies within the last 5 years, with the exception of cervical carcinoma in situ and adequately treated basal cell or squamous cell carcinoma of the skin * Receipt of any investigational agents within 30 days prior to commencing study treatment. * Uncontrollable diarrhea that may affect the ability of the patient to absorb ZD 6474 or tolerate side-effects. Laboratory results: * Adequate bone marrow function as defined by granulocyte count \< 1500/mm\^3 and platelet count \< 100,000 * Serum bilirubin \>1.5x the upper limit of reference range (ULRR) * Serum creatinine \>1.5 x ULRR or creatinine clearance \< 50 mL/minute (calculated by Cockcroft-Gault formula.) * Potassium \< 4.0 mmol/L despite supplementation; serum calcium (ionized or adjusted for albumin,) or magnesium out of normal range despite supplementation. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \> 2.5 X ULRR