A plane isothermal problem of the internal contact between elastic cylindrical bodies separated by a thin layer of a viscous lubricating fluid under constant load and reverse motion is considered. To determine the deformations of the contacting bodies, solutions of the plane problems of the elasticity theory for a cylinder and a space with a cylindrical cut are used. Extreme cases of low load, high load, small and long periods of reverse motion are considered. The dependences of lubricant layer thickness and pressure on the angular coordinate at different times, as well as the dependence of the eccentricity and the minimum lubricant layer thickness on time are presented. It is shown that the minimum lubricant layer thickness as a function of time exhibits a decrease when braking the cylinder and continues to decrease for some time after a change in the direction of rotation and an increase in speed. It has been established that at the times when the speed is low, under high loads, the gap has narrow spots at the boundaries of the high-pressure area, preventing the lubricant from leaking out of the gap. At a low load and a long period of reverse motion, the maximum pressure in the lubricant layer can increase more than twice.