Abstract: The generalized potential solutions of the generalized and homogeneous Biot's equations of consolidation are obtained.The soil grain and fluid compressibilities are taken into account.It is found that when Darcy's seepage coefficient approaches infinitely,the generalized potential solutions of Biot's homogeneous equations degenerate into Papkovich's solutions in classical static elasticicity.When grain and fluid bulk moduli approach infinitely,the simplified Biot's theory of consolidation that does not consider soil grain or fluid volumetric compressibility are obtained.Therefore the generalized potential solutions of the generalized and homogeneous Biot's equations of consolidation degenerate into those of the simplified ones.The generalized expressions of displacements,strains and stresses for general and simplified Biot's equations of consolidation are expressed in terms of the potential functions.