The estimation of surface heat flux density or surface temperature utilizing temperature history inside a heat conduting solid is called the inverse heat conduction problem. The problem becomes nonlinear if the thermal properties are temperature dependent. A numerical method employing a finite difference scheme for solving an inverse problem of rapid transient heat conduction is developed and presented in the thesis. With a given interior temperature as a function of time, by applying the method, a surface temperature function of time is generated through a numerical iterative procedure. Surface heat flux is then found subsequently with a straightforward difference method. The scheme is designed for an arbitrary given temperature function and with arbitrary thermophysical properties. A numerical model is constructed and tested with analytical inputs for linear cases. Comparisons were obtained from selected rapid transient experimental data.