Esophageal stents are used as a clinical method for the treatment of a wide variety of esophageal diseases. Knitted mesh stents have such advantages as high flexibility and ease of production. In this study, an analytical approach was applied to simulate the weft knitted esophageal stents and to investigate the mechanical behavior of these tubular structures against the axial and circumferential stresses by using finite element (FE) and mathematical models. Then, the mechanical properties of the knitted structures were evaluated while the simulated food bolus was passed through the stent channel. The results demonstrated that the FE model had a good performance in simulating the mechanical properties of the esophageal knitted stents. The error of the prediction performance of the FE models was between (10–16)% and (7–11)% for the longitudinal and circumferential directions, respectively. Simulation of the food bolus passage also demonstrated that the esophageal PGA stent wall could tolerate a 7.96 kPa force and a strain of 65% by food bolus; so, it could mimic the real state of esophagus during its application. This model could be applied to design and investigate the mechanical behavior of the knitted stents in clinical application conditions.