Auto Tuning Niching Genetic Algorithm was used to design optimal HTS magnets for the 600 kJ class SMES system under several design constraint conditions. Constraint conditions were operation loss of magnet (less than 2 W), inductance of magnet (less than 24 H), the number of Double Pancake Coils (about 10 DPCs), the number of turns of DPC (less than 300 turns), outer diameter of DPC (close to 800 mm) and total length of HTS wire in a DPC (less than 500 m). As a result of optimum design, we obtained design parameters for the 600 kJ SMES magnet according to two operating currents, 360 A and 370 A. However, even though the HTS magnet was designed optimally in respect to the electromagnetics, consideration of mechanical integrity due to the stress by Lorentz force must not be neglected for the stable operation of the SMES system. Therefore, we developed a program, through the Finite Element Method (FEM), for stress analysis due to Lorentz force in operation of the SMES system. In this paper, the stresses (radial and hoop stress) imposed on the designed HTS magnets were calculated by the program, and the results of stress analysis were discussed.