In this paper, we study the effect of varying permeability on convection in porous media. The basic mathematical framework for convection in porous media governed by Darcy’s Law is outlined. The linear stability analysis is performed to observe convection patterns. The resulting mathematical model is solved by implementing bvp4c in Matlab. In the classical case where permeability is constant, we observe symmetric contours of Bénard convection cells and the critical Rayleigh number is Rac = 4π2 with wave number a = π. As permeability is varied, the critical Rayleigh number and wave number changed. Also the Bénard convection cells are not symmetric in the non-classical setting. We also plotted contours for temperature θ and stream function ψ.