Steady-state and transient ignition problems are solved by the finite element method. Discretized equations for the reactive heat equation are set down using Galerkin’s method. The steady-state discretized equations are solved by an incremental Newton-Raphson procedure using the Frank-Kamenetskii parameter as the incremented or “loading” variable. Critical values of the Frank-Kamenetskii parameter are given for both common and unusual shapes using isoparametric finite elements to describe the geometrical features of the bodies. The transient ignition problem is solved by using the finite element spatial description together with a midinterval time differencing scheme.