Purpose: To evaluate the influence of using polyetheretherketone (PEEK) copings and/or three different dental restorative materials for the success of tooth-and-implant-supported fixed partial dentures (TISFPDs) in the maxillary posterior region under static loading via 3D finite element analysis (3D FEA). Materials and Methods: Six 3D FEA models were designed for the extraction of maxillary first and second molars. The following elements were modeled: bone, implant, abutment, PEEK copings, second premolar, periodontal ligament (PDL), and six three-unit TISFPDs with different restorative materials (porcelain-fused-to metal [PFM], PEEK-composite [PC], monolithic zirconia [MZ]). Then PEEK copings were modeled to be cemented onto the implants as a double-crown system for the first three groups (PFMPEEK, PCPEEK, and MZPEEK), whereas the next three groups (PFM, PC, and MZ) excluded a PEEK coping in their designs. The prostheses were loaded twice—once vertically and once obliquely. From the determined points, 250 N for vertical loading (0 degrees to the long axis) and 200 N for the oblique loading (30 degrees to the long axis) were applied. Von Mises stresses and maximum and minimum principal stress values were analyzed. Results: Regardless of the material used for the suprastructure, the maximum average stress was reduced by the use of PEEK copings. Considering the maximum stress distribution, PC appeared to have the highest stresses on the cortical bone, implant, and screw. Additionally, the von Mises stresses formed in the PDL model were lower when a PEEK coping was included in the design of the TISFPD, reducing the risk of intrusion. Conclusions: The stress distribution was positively affected by the PEEK coping in the TISFPD design, reducing bone resorption and failure. This elastic material generated lower stresses at the bone and implant, and no significant effect was found on stresses around natural teeth.