An effective mathematical method to deal with the viscoplastic lubrication model is presented here by applying the parametric variational principle (Zhong, 1985). The plastic slippage of lubricant would occur at the lubricated surfaces under isothermal lubrication. The boundary tangential velocity, therefore, can be taken as the parametric vector (or the control vector) in variational process. The mathematical model of the original problem is finally reduced to a complementarity problem. The algorithm presented in this paper is simple and reliable and shows promise in engineering application.

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