Friction/stiction and wear are among the main issues in magnetic storage devices and microelectromechanical systems/nanoelectromechanical systems having contact interfaces. A numerical model which simulates the actual contact situations of those devices is needed to obtain optimum design parameters including materials with desired mechanical properties, layers thickness, and to predict and analyze the contact behavior of devices in operation. This study presents a first attempt to develop a numerical three-dimensional multilayered elastic–perfectly plastic rough solids model to investigate the contact behavior under combined normal loading and tangential traction. Energy method is used to formulate the problem, and variational principle in which the contact pressure distributions are those which minimize the total complementary potential energy is applied. A quasi-Newton method is used to find the minimum, and fast Fourier transform is applied to enhance the computation efficiency. In-depth analyses of the effects of friction force, layers properties, and layers thickness to contact statistics and stresses are performed. The optimum layer parameters which decrease friction/stiction and wear are investigated and identified.