This work considers wildfire growth over variable topography. Through an analysis of fire perimeter growth for homogeneous conditions over a surface of constant slope, a mathematical model of fire growth for heterogeneous conditions and variable surface is proposed. The mathematical model is in the form of a system of partial differential equations that require a numerical method of solution. A simple numerical solution technique is described and example solutions are given for fires over a variety of complex surfaces illustrating that simulation results can be obtained in reasonable time.