In this work, we present a new computational model to solve the Black Oil flow model incorporating geomechanical coupling. The extended flow equations, describing the movement of the aqueous, oleic, and gaseous phases, incorporate new complex features associated with transient porosity and are rewritten in a proper Lagrangian formulation giving rise to a new form of the pressure equation with additional source terms stemming from the non-stationary nature of the total mean stress along with a new overall compressibility concept. The flux–pressure system is linearized by a Newton scheme and discretized by a mixed-hybrid finite element method with the lowest order Raviart Thomas element whereas the elasticity subsystem with the additional body force associated with the pressure gradient is also discretized by a mixed formulation based on the decomposition of the effective stress into spherical and deviatoric components. The system of conservation laws for the saturations is discretized by an extended version of a central-upwind finite volume scheme. The potential of the computational model is illustrated in numerical simulations of water-flooding problems in poroelastic media.