<p>The fundamental characteristic of a semi-permeable porous material is that the solvent is allowed to pass through it but the solute is not. Due to this characteristic, a solute concentration gradient can drive chemical osmosis flow in the solution-saturated semi-permeable porous material. Although analytical solutions have been derived for one-dimensional chemical osmosis induced flow and solute concentration variation problems, computational simulations of two-dimensional chemical osmosis induced flow and solute concentration variation problems remain lacking to date. To fill this gap, a new mathematical model is first established, in this paper, for describing two-dimensional chemical osmosis induced flow and solute concentration variation problems in solution-saturated semi-permeable porous materials. Then a computational simulation procedure, which contains the finite difference and finite element methods, is proposed to solve the partial differential equations involved in the established mathematical model. For the purpose of verifying the proposed computational simulation procedure, the analytical solution of a benchmark problem has been derived mathematically. The related computational simulation results have demonstrated that: (1) the proposed computational simulation procedure is correct and accurate for solving chemical osmosis induced flow and solute concentration variation problems; and (2) the applied boundary conditions have significant effects on the computational simulation results of two-dimensional chemical osmosis induced flow and solute concentration variation problems in the solution-saturated semi-permeable porous material.</p>