A posteriori error estimation method for finite element solutions of natural frequencies and natural mode shapes of structures is proposed in this paper. The governing equations of a posteriori error for free vibration problems are introduced. A method used for solving the error equations is presented and an efficient solution strategy is developed since it is difficult to solve the error equations directly. A technique of eliminating the degrees of freedom at the mid-node of element is developed in order to reduce the size of matrix in error equations. The finite element solutions of eigenvalues and eigenvectors are improved by adding the estimated error onto the original solutions.