This chapter presents some results of computer simulation related to the problems in total knee arthroplastyTotal knee arthroplasty (TKA). The simulation uses the movable cellular automaton method, which is a representative of the discrete element approach in solid mechanics and allows correctly simulating mechanical behavior of a variety of elastoplastic materials including fracture and mass mixing. Firstly, the knee joint subjected to osteoarthritis is considered under therapeutic shock waves. The model includes the proximal part of the tibia, the distal part of the femur, the corresponding cartilages, and the meniscus. The biological tissues are simulated using the Boit poroelastic model. The later allows revealing the role of the interstitial biological fluid in the mechanical behavior of the tissues. The bones are considered as a composite consisting of outer cortical and inner cancellous parts. The cartilage and meniscus possess reduced poroelastic properties due to degeneration caused by osteoarthritis. Secondly, the artificial knee joint is considered with metallic prostheses and polymer insert instead of the cartilages and meniscus. Finally, the model of sliding friction between the two rough surfaces of the metallic and polymeric parts of the artificial knee joint is studied at the mesoscale. In the latest study, the roughness is considered explicitly and varied to analyze its role in the wear of the polymeric component.