When a semi-infinite surface is shot peened the in-plane inelastic strains are zero because of compatibility. As a result, the in-plane residual stress and plastic strain are linearly related. These boundary conditions motivate a second order differential equation similar in mathematical form to a modified Kelvin solid model with a strain acceleration term. Solving the resulting equation gives a closed form expression for the plastic strain as a function of time. The plastic strain rate is solved by taking the derivative with respect to time. Comparisons with published finite element data show good agreement and are within 10% for most of the loading and unloading period.