In order to compare numerical and analytical results for the free vibration analysis of Kirchoff plates with both mixed and damaged boundaries, the Chebyshev collocation and perturbation methods are utilized in this paper, where the damaged boundaries are represented by distributed translational and torsional springs. In the Chebyshev collocation method, the convergence studies are performed to determine the sufficient number of the grid points used. In the analytical method, the small perturbation parameter is defined in terms of the damage parameter of the plate, and a sequence of recurrent linear boundary value problems is obtained which is further solved by the separation of variables technique. The results of the two methods are in good agreement for small values of the damage parameter as well as with the results in the literature for the undamaged case. This study can lead to an efficient technique for structural health monitoring (SHM).