In order to solve the conformal contacted rough surface lubricating problem,the finite cell method (FCM) is proposed,which is a deterministic multiscale computational method for heterogeneous problems. The basic principles and key implementation steps are introduced in detail. The proposed method is validated by a number of comparative numerical experiments. Parallel implementation and performance of the method are also addressed. The speed,accuracy of FCM have been systematically analyzed,and the results show that: the computational difference of the results between FEM and FCM are less than 0.2% and the computational scale can be expanded up to three orders of magnitude; Moreover,the computing time can be significantly reduced. Therefore,the FCM is a practical numerical method for calculating the rough surface lubrication problems. Furthermore,FCM can also be applicable in other engineering fields,such as porous flow and heat transfer.