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The paper presents the dynamic characteristics of thin cylindrical shells subjected to unpressurized and pressurized conditions. Emphasis is given to develop theoretical models based on LOVE's first approximations and Donnell's assumptions to the higher order linear differential equations of thin cylindrical shell governing equations to determine Eigen values and Eigen Vectors of the shells subjected to uniform internal pressure. The characteristic equation thus obtained from model is a cubic equation and results in three roots for the three dimensional shell. Axial, circumferential and radial frequencies and mode shapes are generated for different pressurized conditions. The variation of radial frequency at higher values of circumferential nodes is predominant as compared to axial and circumferential frequencies. Numerical techniques for pressurized conditions are computed to compare with the theoretical model developed.

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