<p>The elastic transmission eigenvalue problem is fundamental to the qualitative methods for inverse scattering involving penetrable obstacles. Although simply stated as a coupled pair of elastodynamic wave equations, the elastic transmission eigenvalue problem is neither self-adjoint nor elliptic. The aim of this work is to provide a systematic spectral approximation analysis for the VEM of the elastic transmission eigenvalue problem with equal elastic tensors. Considering standard assumptions on polygonal/polyhedral meshes, we prove the stability analysis of the associated VEM bilinear forms, which shall be applied to the well-defined property of the discrete solution operator. Then the correct approximation of spectrum for the proposed VEM scheme is proven. Necessitated by supporting the convergence analysis, a series of numerical examples are reported. In addition, some negative points of the current VEM scheme are considered, including the locking phenomenon and the influence of VEM stabilization parameters. Thanks to the flexibility of construction for the VEM space, the locking-free and stabilization-free VEM approaches are utilized to tackle with these negative aspects.</p>