A two-dimensional finite element model is developed to simulate the interaction between metal samples and laser-induced shock waves. Multiple laser impacts are applied at each location to increase plastically affected depth and compressive stress. The in-depth and surface residual stress profiles are analyzed at various repetition rates and spot sizes. It is found that the residual stress is not sensitive to repetition rate until it reaches a very high level. At extremely high repetition rate (100 MHz), the delay between two shock waves is even shorter than their duration, and there will be shock wave superposition. It is revealed that the interaction of metal with shock wave is significantly different, leading to a different residual stress profile. Stronger residual stress with deeper distribution will be obtained comparing with lower repetition rate cases. The effect of repetition rate at different spot sizes is also studied. It is found that with larger laser spot, the peak compressive residual stress decreases but the distribution is deeper at extremely high repetition rates.