This paper presents a mathematical model for designing cellular manufacturing systems (CMSs) solved by GENETIC ALGORITHMS. This model assumes a dynamic production, a stochastic demand, routing flexibility, and machine flexibility. CMS is an application of group technology (GT) for clustering parts and machines by means of their operational and / or apparent form similarity in different aspects of design and production. Most previous researches carried out in CMSs have been embodied in static production and deterministic demand states. Due to real situations of a CM model, if includes a great number of variables and restrictions requiring a long period of time, memory, and process power in order to be solved using available software packages and current optimal methods. Therefore, most researchers pay attention to novel methods. One of these methods is GENETIC ALGORITHMS (Gas). GA is a class of stochastic search techniques used for solving the NP-complete problems, such as CMSs. In this paper, a nonlinear integer model of CMS is designed in dynamic and stochastic states. Then, GENETIC algorithm is used to solve the problem and finally computational results are compared to existing optimal solutions in order to validate the efficiency of the proposed algorithm.