This paper reports on implementation of several numerical techniques to solve a set of governing equations resulting from simple one dimensional isotropic consolidation of soils that behave according to the Cam clay model. Three different methods of solving the equations of consolidation, namely the collocation method, the finite volume method and the finite element method, are presented. Apart from evaluating their efficiency, which becomes particularly crucial when implementing these techniques in the framework of an optimization problem aimed at tuning the model parameters, a set of parameters of a Cam clay model driving the time dependent response of the soils (deformation dependent variation of the coefficient of permeability and preconsolidation pressure) is also discussed.