The friction between normal synovial joints is so small that it is usually neglected in theoretical or numerical analyses of joint contact problems. Compared to engineering materials, which have much higher coefficients of friction μ of 0.2-2.0, human synovial joints, uniquely, have striking superiority. However, in diseased states, the lubrication quality of cartilage deteriorates, and there is a significant increase in measured interfacial frictional force. In addition, in artificial joints or implant devices, friction exists between contacting bodies, which could cause problems of wear and loosening. The purpose of this study is to investigate the frictional contact problems by formulating a new numerical algorithm in Finite Element Analysis (FEA). Significant effects of the friction on contact stress as well as the contact area are demonstrated with numerical results.