Summary: An approximate method for analyzing the free vibration of rectangular plates with a hole of different shapes is proposed. The shapes of the holes are circular, semi-circular, elliptic, square, rectangular, triangular, rhombic, etc. These rectangular plates with a hole can be considered ultimately as a kind of rectangular plates with non-uniform thickness. A hole in a plate can be considered as an extremely thin part of the plate. Therefore, the free vibration problem of a plate with a hole can be translated into the free vibration problem of the equivalent rectangular plate with non-uniform thickness. For some plates with different-shaped holes the convergency and accuracy of the numerical solutions calculated by the proposed method are investigated.