A back propagation neural networking Volterra nonlinear system（BPNNVNS） was used to modeling and simulate residual stress distributions in cylindrical grinding under various grinding process parameters and grinding dynamics. Prediction of the magnitude of the residual stress and tensile peak location was implemented, the nonlinear superposition relationship in the residual stress distribution due to the number of grinding passes was verified, and the calculation of residual stress distribution in the subsurface of cylindrical grinding was achieved. The excitation function of BP neural network in three layers was decomposed with Taylor series on peaks to resolve all nucleus of Volterra series, the discrete Volterra network learning algorithm was used to achieve modeling of the nonlinear residual stress in cylindrical grinding dynamic system. An experiment is used for the model development and validation. 