Abstract: The finite element method of lines (FEMOL) is a general and powerful semi-discretized method for BVPs. By viewing it as a generalized one-dimensional method, the well-established Element Energy Projection (EEP) method for super-convergence computation and the corresponding self-adaptive strategy in one-dimensional FEM can readily be incorporated into FEMOL, making the semi-discretized method to be a fully analytical and numerically exact method. Based on the earlier successful implementation of linear self-adaptive strategy in two-dimensional FEMOL analysis, the present paper intends to give a brief report of recent success and progress in adaptively solving two-dimensional free vibration problems. The paper briefly describes the main ideas of the self-adaptive strategy in the two-dimensional FEMOL analysis of free vibration problems, which forms a clean, simple, effective and reliable algorithm that can adaptively produce FEMOL results with accuracy of both the frequency and the mode satisfying the user specified error tolerance in a most restrict form. The numerical examples given show that the proposed method is highly efficient, stable, general and reliable.