In order to obtain the end face engagement worm gear（ hereinafter called as EWG）,which has the features of small volume,rational structure and large bearing capacity,by using the finite element and elasticity theory,the three-dimensional finite element model of EWG is set up. Based on the theory of dynamics and modal analysis,the modal parameters for natural frequency and main vibration mode of EWG are obtained.At last,based on the response surface method of WORKBENCH,taking the first natural frequency and volume as optimization objective,the rational compact structure and large bear capacity of EWG is obtained by multidimensional optimization design. The analysis results show that the volume of the worm reduced by 15. 5%,which guarantee the dynamic property. The results provide basis for modal test,transient analysis and process and manufacturing.