We discuss the computational aspects of a porous flow past a reacting solid undergoing pyrolysis. We present governing equations and develop an accurate numerical method for their solution. The algorithm accurately calculates the rapidly varying component and uses a fixed step size commensurate with the smoothly varying component of the solution. The resulting nonlinear equation is solved with Newton's method; the linear system is solved using a discrete analog of the invariant-imbedding method for second-order, linear, two-point boundary-value problems. We also develop a criterion for truncating the computational domain to minimize the calculational effort, and we present some typical calculations showing that the scheme is accurate and efficient.