Soil in general is not a linear material, in which the relation between stress and strain is more complicated than the simple, linearly elastic relation. To make accurate deformation analysis of clay deposits, the incremental Biot's theory of consolidation is used together with elasto-viscoplastic constitutive relations based on the critical state concept using the modified Cam-clay model. One and two dimensional consolidation problems were analyzed numerically by the infinite-finite elements. Results show that the proposed method can describe the effect of sample thickness on consolidation phenomena. Also the two dimensional behavior of a clay foundation during the construction of embankment was analyzed.