Abstract: Free vibration reflects the dynamic characteristics of structures, serving as a basis for seismic analysis and structural design. In recent years, the adaptive finite element (FE) analysis of both linear elastic and nonlinear problems based on element energy projection (EEP) super-convergent technique has achieved remarkable success and a strategy for adaptive finite element method of lines (FEMOL) has also been developed for 2D free vibration problems. On this basis, a new adaptive strategy for FE analysis of 2D free vibration problems is initially proposed in this paper. By linearizing eigenvalue problems into a series of linear problems, the existing EEP-based adaptive strategy for 2D linear problems has been well incorporated. The algorithm yields natural frequencies with required accuracy and mode functions with the accuracy satisfying the user-preset tolerance in maximum norm. Taking elastic membrane as a model problem, the paper gives an up-to-date report of the new progress and presents a number of typical numerical examples to show the validity and reliability of the proposed method.