Disc couplings present fatigue failure due to cyclic stresses arising from angular misalignment at the metallic flexible disc, even in the presence of lateral misalignment. In rotating machinery, these components are successively subjected to alternate stresses due to misalignment accommodation between coaxial shafts under cyclic motion. The dynamic load in operational conditions leads to a fatigue process through crack propagation, consequently leading to an accumulated fault probability that depends on the number of cycles. Estimating life and replacement mean times during operation is crucial, avoiding downtimes that harm large-scale industrial production. Initially, it is mandatory to conduct a theoretical assessment of the static coupling reliability by cycle, based on the Von Mises stresses under misalignment. The numerical model for those applications demands as high representativeness and accuracy as possible. Therefore, developing such a computational model of disc coupling under angular misalignment is proposed in this work, focusing on mesh refinement by reliability criteria. Convergence criteria based on maximum Von Mises stress can be generally obtained in commercial software. Therefore, a reliability study based on the development of static loading failure criteria for ductile materials is proposed as an alternative convergence criterion for the structural numerical simulations, namely, a statistical safety factor. The proposed convergence criterion is useful to determine mesh refinement that guarantees high design reliability, especially when experimental results are not available to validate the numerical model.