Abstract: Based on some assumptions for the relationship between permeability and void ratio and between effective stress and void ratio of the clay, the non linear equation governing the progress of one dimensional consolidation of the saturated clay, namely Gibson’s Equation, is discussed under different initial and boundary conditions. The properties of different kinds of transformed boundaries are evaluated. It is shown that for some relatively simple conditions, exact analytical solutions of the non linear consolidation equation can be obtained by using the approach of the transformation of Lie group. Finally, the solution obtained in this paper is compared with Tan & Scott’s solutions, and some problems that appeared in solutions are analyzed.