Hybrid prostheses have recently been used as suitable treatment alternatives for edentulous individuals to restore the mastication mechanism. These prostheses utilize “All on four” concept, in which four implants are inserted into the jaw bone, and supported by a bar. Titanium is usually used in the fabrication of “All on four” parts due to its good mechanical properties. However, it has many drawbacks including esthetic impairment, casting issues, hypersensitivity reactions, stress shielding, and incompatibility with imaging techniques. These drawbacks have prompted researchers to find alternative materials (e.g., polymers). Recently, the new polymeric material PEEK has a major role in dentistry, due to its biocompatibility, shock-absorbing ability, and good mechanical properties. This work used the finite-element method to conduct stress–strain analysis on mandible rehabilitated with a hybrid prosthesis, using PEEK in the fabrication of “All on four” parts instead of titanium, using different densities of spongy bone. As the density of spongy bone is expected to influence the choice of “All on four” fabrication material. A 300 N vertical force was applied unilaterally, bilaterally, and anteriorly to stimulate the different mastication mechanisms. The results illustrated that PEEK material reduced the stresses and strains on bone tissues and increased the mucosal stress, compared to titanium. Consequently, this material was recommended to be used in the fabrication of “All on four” parts, especially in the low-density model. However, further research on PEEK implants and abutments is required in near future.