The main objective of this study is to perform the passive balancing of a rotating mechanical system having multi-discs. Reducing the bearing vibrations is considered an optimization problem, and the Genetic Algorithm (GA) approach is used for solving it under the appropriate constraints. Therefore, bearing amplitudes are formulated as an objective function, and the eccentricity directions of 2nd, 3rd,..., nth discs are defined as design variables relative to the first one. The conditions making the forces at the bearings minimum are taken as the nonlinear constraints in the optimization process. On the other hand, a rotating mechanical system having three unbalanced discs is evaluated as a numerical example to show the effectiveness of the proposed approach. Commercial software, ADAMS, is also used for simulating the system and testing the accuracy of the obtained values for the design variables. Theoretical and simulation results show that the proposed approach gives a certain decrease in bearing amplitudes and forces. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B. V. All rights reserved.