A technique of calculating the evolution of turbulence during the combustion phase of a reciprocating engine cycle is presented. The method is based on a local linearization of the full non-linear equations of motion. It is valid when the turbulence is distorted more rapidly by the changes in mean flows than it interacts with itself. The theory requires as input strain rates of the deterministic mean motion, and the initial state of turbulence.Calculations are presented for the particular case of a cylindrical chamber geometry. In the burning process it is assumed that the spark plug is located on the cylinder axis and the strain field is that established by the flame front. The theory calculates the turbulence parameters during the combustion period. Combustion rates, and durations, as a function of equivalence ratio and the initial turbulent and thermodynamic conditions. Calculations were done using various theories of combustion that provide a relationship between the turbulent flame speed and the turbulence parameters. Comparisons are made between the theory and available experimental data and show reasonable agreement.