Polyetheretherketone (PEEK) is a new material used for the frameworks of removable partial dentures (RPD). The questions whether the PEEK framework has similar stress distribution on oral tissue and displacement under masticatory forces as titanium alloy (Ti-6Al-4V) or cobalt-chromium alloy (CoCr) remain unclear and worth exploring. A patient's intraoral data were obtained via CBCT and master model scan. Four RPDs were designed by 3Shape dental system, and the models were processed by three-dimensional finite element analysis. Among three materials tested, PEEK has the lowest maximum von Mises stress (VMS) on periodontal ligament (PDL), the greatest maximum VMS on mucosa, the maximum displacement on free-end of framework, and the lowest maximum VMS on framework. Results suggested that PEEK framework has a good protective effect on PDL, suggesting applications for patients with poor periodontal conditions. However, the maximum displacement of the free-end under masticatory force is not conducive for denture stability, along with large stress on the mucosa indicate that PEEK is unsuitable for patients with more loss of posterior teeth with free-end edentulism.