The fundamental frequency maximization of beam structures is carried out by using strain energy based topology optimization technique. It mainly uses the modal strain energy distributions induced by the mode shapes of the structures. The modal strain energy to be minimized is employed as the objective function and the initial volume of structures is adopted as the constraint function. The resizing algorithm devised from the optimality criteria method is used to update the hole size of the cell existing in each finite element. The beams with three different boundary conditions are used to investigate the optimum topologies against natural mode shapes. From numerical test, it is found to be that the optimum topologies of the beams produced by the adopted technique have hugh increases in some values of natural frequencies and especially the technique is very effective to maximize the fundamental frequency of the structures.