With enhanced performance of computing facilities the iterative design of phase diffractive optical elements (DOEs) has become widely accepted. A great number of up-to-date technologies for DOE fabrication make use of the approximation of the commonly continous DOE phase function by a picewise continuos (quantized) function. This is the reason why constructing iterative procedures for the design of quantized DOEs (DOEs with quiantized phase function) has become topical. Designing quantized DOEs with small number of quantization levels using Fienup-type iterative algorithms (or IFTA-algorithms) is hampered by the necessity to solve the diffractive theory inverse task at every iteration. Besides, using of such algorithms cannot guarantee convergence to global optimum. The use of stochastic procedures does not make it necessary to solve the inverse task. This paper deals with application of the known genetic stochastic procedure to determine the optimum of the function of many variables to designing quantized DOEs forming pre-given intensity distribution along an axial focal zone. Computer simulation results as well as experimental results are presented.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.