In the thesis lubrication and wear at metal/HDPE contacts was addressed. In particular this type of contact occurs in artificial joint replacements. Wear of HDPE was recognized as a major factor limiting device performance. In the thesis, fully implicit fully coupled numerical approach was developed to simulate lubrication and wear. Approach allows solving stationary and transient problems for rough surfaces in a wide range of parameters. Wear coefficients were estimated from experimental data. Wear particles formed in wear process were investigated. Particles were found to be approximately 100 nm in diameter and spherical in shape. Considering theoretical solutions, it was concluded that debris may play a role of third-body abrasive wear particles. In the summary section, some discussion was provided on the topic of theoretical modeling of friction and wear and recommendations for future research were formulated.