The free convective flow and heat transfer, within the framework of Boussinesq approximation, in an anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Brinkman extended non-Darcy flow model. The studies involve simultaneous consideration of hydrodynamic and thermal anisotropy. The flow and temperature fields in general are governed by, Ra, the Rayleigh number, AR, the aspect ratio of the slab, K*, the permeability ratio and k*, the thermal conductivity ratio, and Da, Darcy number. Numerical solutions employing the successive accelerated replacement ( SAR) scheme have been obtained for 100 <= Ra <= 1000, 0.5 <= AR <= 5, 0.5 <= K* <= 5, 0.5 <= k* <= 5, and 0 <= Da <= 0.1. It has been found that (Nu) over bar, average Nusselt number increases with increase in K* and decreases as k* increases. However, the magnitude of the change in (Nu) over bar depends on the parameter Da, characterizing the Brinkman extended non-Darcy flow.