The formation of null basis for equilibrium matrix is the most important part of the finite element analysis when the force method is utilized. For an optimal analysis, the selected null basis matrices should be sparse and banded leading to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient algorithm is developed for the formation of null basis of triangular and rectangular plate bending finite element models, corresponding to highly sparse flexibility matrices. This is achieved by applying a modified ant colony system. An integer linear programming formulation is also presented to evaluate the quality of the results obtained by the proposed ant colony system algorithm. The efficiency of the present algorithm is illustrated through some examples.