From the basic equations of thin cylindrical shells consistent with Love’s first approximation, three uncoupled displacement equations of motion are deduced, the effect of rotary inertia being neglected. Comparison is made with the works of other authors who have used a variety of approximations in arriving at the equations of motion of cylindrical shells. Thus, in a qualitative manner, further insight is gained as to the effectiveness and practicality of these approximations in the solutions of problems of cylindrical shells.