This paper describes the use of genetic algorithms (GA) for solving the facility layout problem (FLP) within manufacturing systems' design. The paper considers a specific heuristic layout planning method, known as the modified triangle method. This method seeks for an optimal layout solution based on the degrees of flows between workstations. The search for an optimal solution is extremely time-consuming and not suitable for larger systems; therefore we have developed a system based on evolutionary computation. Our paper presents a system, based on GA, and the results obtained regarding several numerical cases from the literature. We propose the usage of this system by presenting numerous advantages over other methods of solving FLP for problem representation and evolutionary computation for solution search.