This book deals with the study of the free vibration and buckling of buried cylindrical shell structures. These shells are modelled as circular cylindrical shells embedded in elastic medium. These problems are analyzed from all the available various shell theories. Governing equations of the shells are obtained from the variational principles. Symbolic solutions of the various shell theories to obtain natural frequencies are presented via MATLAB computation. Wave propagation approach is used to solve both the buckling and vibration problems. A generalized MATLAB code is also presented for the study of the vibration and buckling of buried shells. The book will be very much useful for the post graduate students and research scholars, those who are working in the various branches of mechanical engineering.