<p>The analytical and numerical studies on the nonlinear free vibration of a piezoelectric semiconductor (PS) cylindrical shell are carried out within the framework of the first-order shear deformation theory and PS theory. The nonlinear vibration governing equations of the PS cylindrical shell are achieved by using the condition of charge continuity and Hamilton’s principle. The analytical and numerical solutions of the nonlinear vibration responses are obtained by using the harmonic balance method and Runge–Kutta method to solve the governing equations, respectively. Through numerical examples, the influence of the initial electron concentration, radius-to-thickness ratio, length-to-thickness ratio, initial displacement, geometric linearity and geometric nonlinearity on the nonlinear vibration frequency and displacement–time curves is shown in detail. The main innovation of the current study is that the analytical solutions of the nonlinear vibration responses are presented and the difference between the linear vibration and the nonlinear vibration is illustrated. The calculating results also indicate that the vibration attenuation of the PS cylindrical shell may be effectively controlled by selecting an appropriate initial electron concentration and geometric parameter.</p>