Abstract The artificial no-slip boundary conditions on the liquid/solid interfaces are traditionally used widely. Due to the advances on the measurement technique and interface sciences, the applications of no-slip boundary conditions on micro-systems are challenged continuously. The ‘slip effects’ are observed in small clearance measurement or by treating the surfaces hydrophobic. The non-Newtonian power-law fluid as well as the Navier-slip boundary conditions is considered in the partially wetted bearings. A perturbation technique is utilized to derive the extended Reynolds equations. The analysis applied either to Couette–dominated highly non-Newtonian fluids, or to Newtonian fluids with arbitrary Couette-Poiseuille components. Finally, the effects of slip parameters on the bearing performances are discussed.