Neural networks were applied to the estimation of the natural frequencies of symmetrically laminated rectangular plates with all edges clamped. The networks were employed to determine the relationships between the natural frequency data obtained from the extended Kantorovich method by training. After a successful training, the neutral networks generated a new algorithm based on the root mean square error. To verify the accuracy of the new algorithm, it was tested with the new data. The results show the new algorithm's ability to estimate the natural frequencies within an acceptable accuracy range.