Abstract: To suppress gray-scale elements in topology optimization for continuum structures,two modified heuristic optimality criterion methods are proposed.These methods can be used in conjunction with the SIMP material description.Gray-scale elements are compelled to be 0 or 1 by utilizing the smooth Heaviside function.At each optimization iteration step,the volume constraint function can be satisfied naturally.Not only gray elements are suppressed,but also the efficiency of optimization solving is improved with the proposed methods.The validity of the proposed methods and strategy are substantiated by several typical two-dimensional topology optimization problems.