Abstract: A mathematic model for topology optimization of continuum structures is developed using SIMP interpolation scheme and the method of moving asymptotes(MMA) in the paper. The intermediate density in optimized structure is investigated, and a rational range for exponent of SIMP model is obtained. The numerical instability problems such as checkerboards and mesh dependencies are also discussed, and these numerical problems are settled through a kind of sensitive filter method. The flowchart for topology optimization is figured out, and a simple software for two dimensional linear elastic structures is developed. The optimal results of several examples show the efficiency of these methods proposed in the paper.