Manufacturing Cell Design problem has been a research area in the cellular manufacturing context since 1970s. Prior to the 1990s, the problem had been examined basically with respect to only a single criterion, e.g.: minimizing intercellular parts movements, maximizing similarity among the parts and/or machines in the cells, minimizing imbalance of the work load among the cells. In the 1990s and after, a number of papers have been published that model the cell design problem as a Multi-Criterion Decision Making (MCDM) problem, in particular as a Multiobjective Optimization Problem (MOP). In this thesis a new multiobjective model has been developed to deal with the exceptional elements in the design of a Cellular Manufacturing System. The set of objectives include: minimizing intercellular part movements, minimizing sum of machine duplication and part subcontracting cost, minimizing machinery underutilization and minimizing imbalance of the cells workloads. Due to the conflicts among the objectives, attaining an ideal solution, i.e. a solution that simultaneously optimizes all of the objectives, is impossible. However a set of non-dominated (or Pareto Optimal) solutions could be sought from which the decision maker will be able to select based on his or her priorities. To this end, a multiobjective genetic algorithm called XGA was developed and coded in Visual C++. The algorithm makes use of the non-dominated sorting idea to rank individuals in the population. An extension of Reminder Stochastic Sampling Without Replacement (RSSWP) is developed wherein a novel probabilistic scheme of elitism is applied. Niching is employed to keep diversity among the individuals in the elite set. Stopping criteria of the algorithm is devised so that takes into account convergence of the algorithm to the Pareto-Optimal frontier along with the maximum number of generations. A number of cell design problems taken from the literature were solved by the XGA and also by three reference algorithms, namely: VEGA, NPGA and NSGA. The results obtained by the XGA show promising improvements in three dimensions, i.e. quality, diversity and CPU time compared with the reference algorithms.