A method which estimates a posteriori error in finite element solutions for dynamic plate bending problems is proposed in this paper. There are two kinds of discretizations, one is for space domain and the other is for time domain, for dynamic finite element analysis. In this paper, a posteriori error due to discretization in space domain is mainly considered. The governing equation of a posteriori error for plate bending problems is introduced based on the theory derived by Ohtsubo et. al. A posteriori error in each time step is under our consideration, while the elapsed a posteriori error from the initial time to an arbitrary time is not investigated here. In order to see the validity of the proposed method, two numerical examples are solved. Good agreements of estimated a posteriori error with referred error are observed.