The dynamic instability of cylindrical shell with clamped-free boundary condition subjected to constant follower force or $P_0 + P_1cos {Omega}_t$ type pulsating follower force is analyzed. The motion of shell is modeled using the shell theory considering rotary inertia and shear deformation, and analyzed with finite element method. In case of constant follower force, the changes of eigenvalues dependent on the magnitude of applied load are investigated and the critical loads are obtained. In case pulsating follower force, instability regions of exicitation frequency are obtained by modal transform with right and left modal matrix and by multiple scales method. The effects of thickness ratio and aspect ratio on the instability of shell are studied.