In the paper, the flow of a Newtonian type of lubricant in the clearance of a curvilinear bearing is considered. It is assumed that the bearing walls are modelled as smooth and impermeable. In analytical considerations, full inertia of the longitudinal flow and partial inertia of the circumferential flow are taken into account. The equation of motion of the lubricant is solved by the modified method of averaged inertia. A thrust bearing and spherical bearing are considered, for which dimensionless pressure distributions and the bearing capacity are given.