Abstarct: Natural convection by combied heat and mass transfer with opposing horizontal heat and solute gradient has been investigate in an anisotropic porous cavity using the Darcy model.The porous medium is assumed to be both hydrodynamically and thermally anisotropic.The principle direction of the permeability tensor are taken oblique to the gravity vector,while those of thermal and solutal diffusivity coincide with horizontal and vertical coordinate axes.In the present study,natural convection in a porous cavity is investigated numerically by finite element method.It is assumed that a non-isothermal occurs,which may lead to make internal heat generation in the cavity.The source term in the energy equation is proportional to the generation rate of solute concentration governed by a Monod model.It is assumed that the vertical wall are at constant temperatures and bottom wall and top wall is with the isothermal temperatures.This problem is concerned for both cases,that in the one case the porous cavity is assumed to be a non-homogenous with thermal equilibrium.principle points of permeability tensor build with gravitate vector oblique angle ,so that for thermal and solute tensor of points its coincide with vectors horizontal and vertical. Hence, it is useful to consider a general permeability tensor.The second order permeability tensor, is diagonal in the coordinate system with the diagonal components , . Since the media is anisotropic, therefore diffusion properties are also anisotropic in nature. However, because of our main focus (anisotropic permeability) and in order to reduce the number of influencing parameters, diffusivity tensors with principle directions coinciding with and axes have been preferred. Also average nuselt number value on left wall calculated. Fluid in cavity incompressive, Newtonian and use darcy model of momentum equation.fluid flow two dimention and no steady state.