To solve the large computation and low efficiency of stress approximation in structural topology optimization with stress constraints,a method of the first-order approximation of internal force is put forward to express explicitly stress constraints.And the comparison with the full stress method（ that is,the zero-order approximation of internal force） and the first-order approximation of stress with reciprocal variable is carried on. Their advantages and disadvantages,and their effect on the solution efficiency are studied. To illustrate and analysis clearly iterative history data of the design variables,the objective function and constraints for different methods of stress constraint approximation during the optimization process,the design variable linking technology is adopted to reduce the number of design variables in topology optimization examples with stress constraints. The results of the topology optimization show that the first-order approximate of internal force is better than full stress method and the first-order approximation of stress with reciprocal variable. The number of iterations is the least. The solution efficiency is the highest. The optimal structure is the lightest.