This paper addresses an analytical approach to tolerance and reliability analysis of mechanical systems with uncertainty. Many mechanical systems consist of links and lubricated joints. The mobility method is applied to consider lubrication effects and the clearance vector model is used to stochastically define a mechanism for tolerance and reliability analysis. To show the validity of the proposed method, a four-bar path generator and a slider-crank mechanism are considered. The results obtained by applying the proposed method are compared with those by Monte-Carlo simulation.