An analysis of grain ignition and flame spreading in solid-propellant rocket engines was performed to calculate chamber pressure as a function of time during this phase. Assumed for the analysis were isothermal one-dimensional gas flow in the chamber, spatially uniform gas pressure, two-dimensional transient heat conduction in the grain, perfect gas properties, choked nozzle flow, and gas generation due only to grain surface deflagration. Also investigated is the case of a diaphragm stretched across the throat entrance which bursts with sufficient pressure build-up. Initial conditions include instantaneous gasless ignition of a section of the upstream end of the grain, uniform pressure and temperature in the gas, a uniformly distributed temperature in the unignited portion of the grain, and an axially varying gas velocity distribution. A quasi-analytic solution (analytic in each time step) for chamber pressure is coupled, through changes in the burning wall area, to a finite difference solution for grain temperature (using the stable Peaceman-Rachford alternating direction method). After the end of flame spreading, the pressure calculation alone is continued until steady-state conditions are approximated. A computer program was written to perform the calculating for varying input data.