A study is made of natural convection heat transfer in a cavity filled with an anisotropic porous medium. The vertical walls are respectively heated and cooled isothermally, while the top and bottom walls are adi-abatic. The porous medium is anisotropic in thermal conductivity with its principal axes oriented in a direction that is oblique to the gravity vector. Governing parameters of the problem under study are the Rayleigh number R, aspect ratio of the cavity A, the thermal conductivity ratio k* and the angle of the principal axis θ. A numerical study is performed to assess and extend the results of the analytical predictions.