Fretting is a surface damage phenomenon associated with different fields like tribology, contact mechanics, and material science. Fretting damage can be seen in mechanical joints like bolted and gasket joints of internal combustion (IC) engines. The steel plate head gasket joint has exhibited intermittent gasket fretting issues on some legacy industrial engines. To minimize the fretting damage risk to the steel gasket, full factorial Design of Experiment (DOE) based on Ruiz parameter (FDP/F1) is carried out to identify an optimized liner bite ring geometry (liner’s design feature at the interface with the steel gasket) within the bolted joint. DOE-predicted results based on two-dimensional (2D) axisymmetric finite element analysis (FEA) are further validated using full three-dimensional (3D) FEA, with the boundary conditions consistent with the operating conditions known to accompany the fretting damage. In addition, Bayesian regularization (BR)-based backpropagation neural network (BPNN) models are considered to predict Ruiz parameters for the nominal and optimized liner geometries. Overall, a good correlation is observed in terms of the predicted F1 results using 2D FEA, full factorial DOE, BR-BPNN, and 3D FEA. Also with the considered approach of carrying out DOE based on 2D FEA results to obtain the optimized liner geometry helped significantly in terms of the simulation run time.