This paper presents a semi-analytical solution for one dimensional consolidation problem of inelastic clays under cyclic loading considering the effect of the change of the consolidation coefficient of the soil layer. Due to change of the consolidation coefficient, and time-dependant loading, Terzaghi's theory would not be applicable in cyclic conditions. In this research, a method based on the time variable exchange along with the superimposing rule is employed to overcome these shortcomings. Changes in the consolidation coefficient are applied in the solution by modifying the loading and unloading durations introducing a Virtual Time. Based on the superimposing rule a set of continuous static loads in specified times are used instead of the cyclic load in the transformed time space. Each full cycle of loading is replaced by a pair of static loads with different signs. Based on the Terzaghi's theory the porewater pressure distribution and the degree of consolidation are calculated for each static load and the results are superimposed. A set of laboratory consolidation tests under cyclic load and numerical analysis are performed in order to verify the presented method. The numerical solution and laboratory tests results showed the accuracy of the presented method.