Abstract: Pseudo modes may appear in topology optimization of continua when the SIMP (Solid Isotropic Material with Penalization) material model is used for eigenvalue problems. A new method based on the combined use of the frequency shift technique and pseudo mode identification is proposed to eliminate the detrimental effect of such pseudo modes. The topology optimization of continuum structures for maximum fundamental frequency subjected to volume constraint is considered in the study. The nodal densities are taken as design variables to describe the material distribution in the design domain. Based on an investigation of the characteristics of pseudo vibration modes, the eigenvalue shift technique is suggested for avoiding low-order pseudo modes with small eigenvalues from the eigenmode extraction, and further a pseudo mode identification criterion is constructed to exclude other high-order pseudo modes. A highly efficient and reliable algorithm for the topology optimization is then made possible. Numerical examples are presented illustrating the effectiveness of the proposed method.