The finite element method was applied to the natural frequency analysis of arbitrary shell structures. A computer program based on the isoparametric thick-shell element was developed. The program was tested against several plate and shell problems. The results were compared with the experimental and numerical results reported by other researchers with excellent agreement in most cases and fair agreement in others. An oval cross-section hollow blade was analysed in detail both numerically and experimentally. The experimental model could not match the design geometry due to manufacturing difficulties. The numerical analysis was first performed on the nominal geometry which lead to a regular set of modes. Later, the numerical model was corrected to match the experimental model, and satisfactory agreement was obtained between the results for the lower modes of vibration. Other topics which could be studied as an extension of this work were pointed out, and some exercises were performed on them without given any experimental verification. Finally a hollow turbine blade was analysed and very good results were obtained.