In engineering practice, the classic finite element method encounters the intractable problem in reaching an adequate mesh to acquire reliable results, which brings difficulties in solving large and complex structures. Recently, a series of overlapping finite elements have been proposed to improve the solution quality from the low-order finite elements, whereas, more researches on these elements in dynamic analyses are still needed. In this work, the behaviors of the overlapping finite element method (OFEM) in the dynamic analysis are first evaluated, and the implicit Bathe time integration method, which is unconditionally stable, is employed to obtain the transient response results in forced vibration problems. From some representative numerical tests, the computation precision and the numerical stability of the OFEM are carefully discussed. The results from these tests show that compared with the traditional finite elements, the overlapping elements are nearly distortion insensitive and can generate accurate solutions with high computation efficiency. Moreover, because only three-node triangular elements are used in the analysis, the computational domain can be discretized without additional user interventions.