A singular finite element (three-noded triangular and four-noded isoparametric element), which has a stress singularity, proposed by Akin was investigated in this paper. The singular elment is incorporated into a usual finite element program which can analyze eigenvalues of the two-dimensional elastic body. Using the singular element, in-plane vibration problems of the plate with an edge crack were analyzed. From the results of the numerical simulation, it was confirmed that the singular element was useful for the dynamic problem.