Over the past few decades, in silico modeling of organ systems has significantly furthered our understanding of their physiology and biomechanical function. In spite of the relative importance of the digestive system in normal functioning of the human body, there is a scarcity of high-fidelity models for the upper gastrointestinal tract including the esophagus and the stomach. In this work, we present a detailed numerical model of the upper gastrointestinal tract that not only accounts for the fiber architecture of the muscle walls, but also the multiphasic components they help transport during normal digestive function. Construction details for 3D models of representative stomach geometry are presented along with a simple strategy for assigning circular and longitudinal muscle fiber orientations for each layer. We developed a fully resolved model of the stomach to simulate gastric peristalsis by systematically activating muscle fibers embedded in the stomach. Following this, for the first time, we simulate gravity-driven bolus emptying into the stomach due to density differences between ingested contents and fluid contents of the stomach. Finally, we present a case of retrograde flow of fluid from the stomach into the esophagus, resembling the phenomenon of acid reflux. This detailed computational model of the upper gastrointestinal tract provides a foundation for future models to investigate the biomechanics of acid reflux and probe various strategies for gastric bypass surgeries to address the growing problem of obesity.