The mass and thermal transport in porous media play an important role in many engineering and geological processes. The hydrodynamic and thermal effects are two interesting aspects arising in the research of porous media. This thesis is concerned with numerical investigations of double-diffusive natural convective heat and mass transfer in saturated porous cavities with Soret and Dufour effects. An in-house FORTRAN code, named ALFARHANY, was developed for this study. The Darcy-Brinkman-Forchheimer (generalized) model with the Boussinesq approximation is used to solve the governing equations. In general, for high porosity (more than 0.6), Darcy law is not valid and the effects of inertia and viscosity force should be taken into account. Therefore, the generalized model is extremely suitable in describing all kinds of fluid flow in a porous medium. The numerical model adopted is based on the finite volume approach and the pressure velocity coupling is treated using the SIMPLE/SIMPLER algorithm as well as the alternating direction implicit (ADI) method was employed to solve the energy and species equations.Firstly, the model validation is accomplished through a comparison of the numerical solution with the reliable experimental, analytical/computational studies available in the literature. Additionally, transient conjugate natural convective heat transfer in two-dimensional porous square domain with finite wall thickness is investigated numerically. After that the effect of variable thermal conductivity and porosity investigated numerically for steady conjugate double-diffusive natural convective heat and mass transfer in two-dimensional variable porosity layer sandwiched between two walls. Then the work is extended to include the geometric effects. The results presented for two different studies (square and rectangular cavities) with the effect of inclination angle. Finally, the work is extended to include the Soret and Dufour effects on double-diffusive natural convection heat and mass transfer in a square porous cavity.In general, the results are presented over wide range of non-dimensional parameters including: the modified Rayleigh number (100smaller or equal to Ra* smaller or equal to1000), the Darcy number (10-6smaller or equal to Dasmaller or equal to 10-2), the Lewis number (0.1smaller or equal to Lesmaller or equal to 20), the buoyancy ratio (-5smaller or equal to N smaller or equal to 5), the thermal conductivity ratio (0.1smaller or equal to Kr smaller or equal to 10), the ratio of wall thickness to its height (0.1smaller or equal toD smaller or equal to 0.4), the Soret parameter (-5smaller or equal to Sr smaller or equal to 5), and the Dufour parameter (-2smaller or equal to Df smaller or equal to 2) .