In this work an enriched quadrilateral overlapping finite elements are proposed for the free vibration analysis of two-dimensional linear elastic solids. This quadrilateral overlapping element is augmented by the polynomial functions and the harmonic trigonometric functions and this scheme exhibits no linear dependence issue which is proven to be inevitable in the generalized finite element method using quadrilateral mesh. Due to the augment of the approximation space, the present approach can achieve satisfactory solution accuracy using a coarse mesh. Moreover, these overlapping elements are less sensitive to the mesh distortion than the classic finite element, indicating that the proposed method can evidently decrease the manual efforts in mesh generation. The performance of the present overlapping elements in the free vibration analysis of two-dimensional solids are demonstrated by typical numerical experiments. The results show that the proposed scheme can obtain higher computational efficiency and convergence rate comparing to the traditional finite element method, and a reasonable matrix conditioning can be reached.