Researches on constrained optimization using evolutionary algorithms have been actively studied. However, these reseaches have problems that the stability and the efficiency of the search is low and the ability of escaping from local solutions is inadequate. In this study, we propose the eGA (epsilon constrained GA), which is defined by applying the epsilon constrained method to a genetic algorithm. The eGA adopts the selection where parents are chosen equally and next generation is formed by top individuals from parents and children, uniform crossover, Gaussian mutation and Cauchy mutation. The eGA realizes stable and efficient search that can escape local solutions. The advantage of the eGA is shown by applying the eGA to various type of 13 constrained problems and comparing the results to the results by other methods.