Solving complex real world Multi-Objective Optimization problems is the forte of Multi-Objective Evolutionary Algorithms (MOEA). Such algorithms have been part of many scientific and engineering endeavors. This study applies the NSGA-II and SPEA2 MOEAs to the radar phase coded waveform design problem. The MOEAs are used to generate a series of radar waveform phase codes that have excellent range resolution and Doppler resolution capabilities. The study compares the ability of NSGA-II and SPEA2 to continually evolve (phase code) solutions on the Pareto front for the problem while maintaining a diversity of solutions (phase codes). Results demonstrate that for the radar phase code problem NSGA-II provides a more diverse population of acceptable solutions and therefore a greater number of different viable phase codes when compared to the solutions provided by SPEA2