Abstract: The balance between computational efficiency and accuracy is hard to reach when standard evolutionary structural optimization (ESO) method is used for frequency optimization. This paper proposed the concept of second order sensitivity as well as the equation for its value. Then it was used in a new algorithm for frequency optimization, which is extended from the standard ESO procedure. Finally, a numerical example was given to demonstrate its performance. The results show that the algorithm is very suitable for structural frequency optimization, especially for the first stage of the twostage optimization process, and that it can keep balance, at some level, between efficiency and accuracy.