Mathematical expressions are derived for the histories of the pressure, flame radius, mass fraction burned, and burned and unburned gas temperatures associated with a spherical flame propagating concentrically in a spherical vessel. The equations are solved numerically for a 9.5 pct ch4/air mixture using the best available information for the burning velocity, expansion ratio, and specific heat ratio. Calculated histories are in complete accord with experimental measurements. The accuracy of calculated histories is determined relative to errors in the system parameters, and it is found that a 10-pct error in either the burning velocity or the expansion ratio results in a 40-pct error in the pressure history. A 10-pct error in burned or unburned specific heat ratio results in a 22-pct error in the pressure history. It was further established that the usual assumption of constant specific heat ratio is unacceptable, but equating the burned and unburned specific heat ratios results in no apparent error in the histories. The cubic law (p = kt3 + po) is derived and discussed, and it is found that the law is valid only during the early period (p<2 atm) of flame growth.