The present work concerns a numerical solution of heat transfer in a bidirectional anisotropic cylinder, subjected to a heat flux through the side surface, while the sections are at set temperatures. The presence of temperature cross-derivative term in the governing energy equation of anisotropic medium makes it difficult to resolve by the usual solving techniques and in particular that of separate variables. Therefore a coordinate transformation is used, in order to eliminate this difficulty by reducing the anisotropic heat equation to an equivalent isotropic equation without complicating the boundary conditions but with a more complicated geometry. The alternating-direction implicit finite-difference method (ADI) is used to integrate the isotropic equation. Inverse transformation provides the temporal evolution of the temperature in the anisotropic cylinder, as well as the corresponding steady-state thermal level. A comparative study to the analytical solution of steady heat conduction equation for an orthotropic medium with the developed digital code has been realized and successfully validated. The aim of this paper is the establishment of dimensionless time correlations for the anisotropic medium steady state heat transfer, according to the data of the problem data: main thermal conductivities, anisotropy and the external heat flux.