The medium of heat conduction is seemingly important in the world today and needs to be well understood. This paper looks at the steady state heat conduction in a rectangular plate characterized by Dirichlet boundary conditions. The steady state heat model is formulated based on some assumptions governing this phenomenon. The model which is an elliptic partial differential equation is solved using both analytic and numerical methods. The separable variable method which is an analytic method gives rise to a closed form solution. A comparative study was made by comparing the accuracy of the Finite Difference Method (FDM) and the separable variable method and the relative errors determined. The results obtained from the separable variable method were close to the numerical method. The FDM gives approximate solution with less time and fitting resilience. It is thus concluded that the FDM method allows control over mensurable error.