An optimum design algorithm is developed for linear optimum design of truss structures in this study. Genetic algorithm which is a discrete optimisation method is used for this algorithm. The aim of this algorithm is to design minimum weight truss without violating constraints. Displacement, stress and stability constraints are considered. Finite element method is used in the algorithm to analyse the structures. The computer program is coded in FORTRAN and optimum design of several truss structures made using this program. Results of this study are compared with result of some other studies to indicate efficiency of the program coded in this study.