This paper is concerned with constraint handling techniques in GA integrated structural optimization. A modified version of Joines and Houck's  penalty function method is introduced and studied with respect to discrete optimization of truss structures. Three test cases are designed and numerically examined to reflect three distinct situations of loading and constraints. Certain recommendations are reached for penalty parameter values. Furthermore, the considered penalty function is reformulated to eliminate its shortcomings. The reformulated penalty function is also applied to the three test cases and the results are compared and fully discussed.