In an attempt to describe the basic phenomenon of grout propagation, a continuous model of miscible fluid displacement in deformable saturated porous media is proposed. In order to exhibit the relevance of the hydromechanical coupling during the mass transport, the model encompasses equations of mass transport and the equilibrium equation of the porous medium as a whole. The basic field variables consist in solid displacement vector, fluid pressure and grout concentration. The mathematical formulation results in a highly coupled and non linear system, the solution of which requires specific numerical techniques. The dis-placement - pressure - concentration formulation is discretized in space by application of the weighted resi-dual method. The whole system is then integrated in time by means of the - method. In order to validate our approach, a numerical comparison is done with existing results obtained with a no-deformable porous me-dium model.