We have developed a new method for predicting the distribution of compressive residual stress on and under the weld surface after Water Jet Peeing (WJP). WJP is a practical technology for the preventive maintenance of nuclear power plants. The welds of internal structures of nuclear reactors are subjected to tensile residual stress without any surface treatment. WJP utilizes a cavitating jet to mitigate the generation of Stress Corrosion Cracking (SCC) by changing the residual stress from tensile to compressive. The prediction and confirmation tests of the compressive residual stress are therefore important. We predicted the residual stress improvement by WJP using a combination of a cavitating jet simulation and a residual stress simulation. Impulsive bubble pressure that varied in microseconds in the cavitating jet was numerically simulated with 'bubble flow model'. The distribution of the impulsive bubble pressure was verified with a measurement of bubble collapse location by using multi Acoustic Emission (AE) sensors. The cavitation intensity was estimated by the bubble pressure. The residual stress simulation was conducted on the basis of the input condition obtained from the cavitation intensity. The residual stress distributions on and under the material surface were predicted. The distributions were compared with measured data, and the results confirmed the developed method for predicting the compressive residual stress after WJP was valid.