The present paper is concerned with the motion of fluid layer between two parallel concentric circular plates, when the inertia of fluid is not negligible. We consider the two specific problems to examine the inertia effects one in which an incompressible Newtonian fluid is injected into the gap through the hole located at the center of each plate and the other in which two parallel plates rotate coaxially with arbitrary angular velocities. The method of solution is an asymptotic expansion which is usually employed for the thinfilm lubrication problem in the limit of small but finite Reynolds number based on the gap height. The asymptotic solutions for the two problems considered here provide the inertia induced secondary flow patterns, which in turn determine the inertia contributions to the flow parameters such as the pressure drop, injection flow rate, and torque required to sustain the rotation of each plate.