Abstarct: In this thesis, the natural convection boundary laxyer flow over an arbitrarily inclined flat plate in a saturated porous medium is studied in the presence of heat generation. The wall temperature is kept at a higher value with the power-law variation. Problem is solved for two kind of heat generation. In first case, heat generation varies exponentially, and in the other case, it is proportional to dimensionless temperature with a power function. Darcy-Boussinesq approximation is adopted to account for buoyancy force. An inclination parameter is used such that all cases of the horizontal, Inclined and vertical plates can be described by a single set of transformed boundary laxyer equations. The non-linear coupled parabolic equations have been solved numerically by using an implicit finite-difference scheme, called Keller Box Method, for both positive and negative inclinations of the plate. Also, the similarity equations for the limiting cases of the horizontal and vertical plates are recovered by setting the inclination parameter 0 and 1, respectively. In case of positive inclination, the solution covers all angles of inclination, whilst for negative inclination; the solution exists only for point at which separation occurs there. It is observed that heat generation causes the change in the slope of dimensionless temperature and velocity profiles, and therefore in quantity of Nusselt number and skin friction coefficient. In some cases, these changes also reverse direction of heat transfer. Moreover there is a wonderful match between the numerical solution and similarity solutions for horizontal and vertical plates of each problem.