This chapter attempts to give an introduction to the vibration behavior of thin shells. The dynamic behavior of shells is more complicated than that of plates and beams due to the curvatures which couple the bending and in-plane deformations. This adds a degree of complexity and yields systems of coupled equations. The equations of motion are initially developed for cylindrical shells and are subsequently reduced by assuming that no loads are applied in two directions. Solution procedures for cylindrical shells are presented for both free and forced (using modal expansion) vibrations for a particular set of boundary conditions. Techniques for solving shell problems with different boundary conditions are also presented. Membrane theory of cylindrical shells is also considered for both free and forced vibration problems. Shells of revolution are discussed for spherical as well as shallow spherical shells. The governing equations of motion for the vibration of composite shells are presented using classical lamination theory. Both free and forced vibration scenarios are also discussed.