Fundamental understanding of contact interactions between two surfaces is of paramount importance as surface-surface contact phenomena can be found in a wide range of applications, such as microelectromechanical systems (MEMS), wire bonding in electronic packaging, total joint replacements (TJR), oscillating-slide actuators, bolted and riveted joints, shroud and snubber in turbine blades, and components operating in a microgravity environment. As result of contact interactions, material loss occurs and can lead to undesirable outcomes. Therefore, the primary objective of this dissertation was to develop a finite element method (FEM) based framework to investigate the effects of cyclic normal and shear (friction) traction, coefficient of friction, and surface topography on material damage, removal rate, and failure mechanisms.First, the problem of a rigid flat and a patterned surface pressed against an elastic-plastic half-space exhibiting isotropic strain hardening was analyzed using the FEM to elucidate the development of plasticity. Simulation results in dimensionless form were obtained and discussed to illuminate the effects of geometry, imprint depth, and coefficient of friction on the evolution of plasticity. The deformation due to the impression of the patterned surface was largely affected by the interaction of the stress and strain fields produced by neighboring protrusions, resulting in a three-stage normal force response. Examination of plastic flow of the half-space material into the pattern cavities revealed that cavity filing became prominent with increasing protrusion distance of the patterned surface and decreasing coefficient of friction. This study introduced a computational methodology for fine-tuning key design and process parameters aimed to enhance the efficiency of metal imprinting.Next, a plane-strain FEM model of a rigid cylinder in reciprocating sliding contact with an elastic-plastic half-space exhibiting isotropic strain hardening was introduced to investigate plasticity-induced damage leading to material loss in oscillatory sliding contact. By incorporating a quasi-static, isothermal damage model based on a ductile material failure criterion into the developed FEM model, plasticity-induced cumulative damage was tracked in terms of a dimensionless damage parameter. Numerical results yielded insight into the effects of normal load and coefficient of friction on material loss due to the accumulation of plasticity with oscillation cycles. Specifically, plastic deformation and wear increased with the number of cycles and coefficient of friction due to the intensification of plastic shearing. A non-monotonic increase of wear with normal load was observed, which was explained by the distribution of plastic shear strain produced under high- and low-load oscillatory sliding conditions and the decrease of the fraction of contact area where slip occurred with the increase of the normal load. The developed computational methodology for exploring the evolution of plasticity, damage, and material loss in reciprocating sliding contacts is an effective tool for assessing the effects of load, friction, and material behavior on the mechanical performance of mechanical systems with components experiencing oscillatory contact.Although most engineering surfaces are nominally smooth, they demonstrate random roughness over a wide range of nano/micro-scales. Henceforth, it is imperative to develop numerical models of the material removal rate for engineering interfaces undergoing reciprocating sliding that take into account the effect of the interface topography. To this end, an elastic-plastic contact mechanics analysis of an isotropic strain hardening half-space in oscillatory sliding contact with a rigid surface exhibiting multi-scale roughness characterized by fractal geometry was performed with the FEM. Cumulative damage was tracked by a dimensionless damage parameter and material stiffness degradation was modeled by a degradation parameter depending on fracture energy. Aside from the subsurface stress and plastic strain fields, the effects of fractal parameters (roughness) on the material removal rate were investigated. Contrary to the classical wear law, which predicts a liner dependence of wear rate on normal load, the material removal rate was found to exhibit a nonlinear dependence on normal load due to the occurrence of material interlocking introduced by the increase of surface conformity and the evolution of material loss. The developed model can be used to perform parametric studies of the material loss in mechanical devices operating in reciprocating sliding contact mode.Delamination is a common failure process in layered materials. Thus, to provide insight into this fundamental problem, a contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces in sliding contact was performed. A surface-based cohesive zone model was implemented in the FEM analysis to model surface separation at the interface. Complete delamination was determined by the critical separation distance of interfacial node pairs in mixed-mode loading based on a damage initiation criterion, exemplified by a quadratic relation of the interfacial normal and shear tractions. Linear stiffness degradation was accounted for by a scalar degradation parameter based on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed mode loading critical fracture energy criterion. Numerical results of the delamination profiles, stress fields, and plastic strain in both the surface layer and underlying half-space illuminated the effects of indentation depth and sliding distance on interfacial delamination for different combinations of elastic-plastic properties, cohesive strength, and layer thickness. The introduced model provides a capability for analyzing plasticity-induced cumulative damage in multilayered structures. The investigations comprising this dissertation provide fundamental understanding of the evolution of stresses, plasticity, material loss, and delamination in contact surfaces subjected to normal loading, sliding, and small-amplitude oscillatory contact. The computational models of this work can be extended to study material loss (wear) in various applications involving contact interfaces, such as MEMS, TJR, and high-efficiency gas turbines.