Three-dimensional printing—especially with fused deposition modeling (FDM)—is widely used in the medical field as it enables customization. FDM is versatile owing to the availability of various materials, but selecting the appropriate material for a certain application can be challenging. Understanding materials’ mechanical behaviors, particularly those of polymeric materials, is vital to determining their suitability for a given application. Physical testing with universal testing machines is the most used method for determining the mechanical behaviors of polymers. This method is resource-intensive and requires cylinders for compression testing and unique dumbbell-shaped specimens for tensile testing. Thus, a specialized fixture must be designed to conduct mechanical testing for the customized orthosis, which is costly and time-consuming. Finite element (FE) analysis using an appropriate material model must be performed to identify the mechanical behaviors of a customized shape (e.g., an orthosis). This study analyzed three material models, namely the Bergström–Boyce (BB), three-network (TN), and three-network viscoplastic (TNV) models, to determine the mechanical behaviors of polymer materials for personalized upper limb orthoses and examined three polymer materials: PLA, ABS, and PETG. The models were first calibrated for each material using experimental data. Once the models were calibrated and found to fit the data appropriately, they were employed to examine the customized orthosis’s mechanical behaviors through FE analysis. This approach is innovative in that it predicts the mechanical characteristics of a personalized orthosis by combining theoretical and experimental investigations.