According to the self-synchronous theory with two vibrating electric motors, a translation elliptic shaker is designed, and its finite element model for the sieving box is established. The dynamic behavior analysis of the sieving box is reached with CATIA software. The natural frequencies and modal oscillation modes of the sieving box are calculated, and the stress and deformation distribution in every part of the sieving box under rated load are obtained. All shows that, its structure design is reasonable. Under the designed working conditions, the maximum principal stress of the side boards is 39.7 MPa, and its dynamic strength is satisfied. The calculating results will be of significance to the design improvement, and give a basis for the experiment research of dynamic strength.