Surface treatment methods, such as shot peening or laser shock peening, are generally used to introduce superficial compressive residual stresses in mechanical parts. These processes are carried out during the manufacturing steps or for the purpose of repairing. The compressive residual stresses prevent the initiation and growth of cracks and thus improve the fatigue life of mechanical components. Electromagnetic pulse peening (EMP) is an innovative process that could be used to introduce compressive residual stresses in conductive materials. It acts by generating a high transient electromagnetic field near the working surface. In this paper, the EMP process is presented and a sequentially coupled electromagnetic and mechanical model is developed for its simulation. This 2D axisymmetric model is set up with the commercial finite element software SYSWELD. After description and validation, the numerical model is used to simulate a case of introducing residual stresses of compression in a nickel-based alloy 690 thick sample, by the means of electromagnetic pulses. The results are presented in terms of effective plastic strain and residual mean stress. The influence of the process parameters, such as current intensity and frequency, on the results is analyzed. Finally, the predictability of the process is shown by several correlation studies.