<p>The nonlinear dynamic behavior and primary resonance of star-shaped auxetic cylindrical shells for large deformations are considered. First, the extensional and bending stiffness matrices are introduced in a closed-form relation for the star-shaped auxetic pattern. For this end, Castigliano’s theorem as well as the homogenization technique are applied. According to the classical theory of thin shells, including von Karman’s nonlinear terms, the governing equations of a star-shaped auxetic cylindrical shell are extracted. The Runge–Kutta and multiple scale methods are employed to solve the nonlinear equations of motion of the auxetic cylindrical shell for the Navier-type boundary conditions. The accuracy and stability of solutions are examined by the finite element analysis. The effects of geometrical parameters of a star-shaped auxetic cylinder on its linear and nonlinear vibrations are investigated. The presented mathematical procedure for linear and nonlinear vibration behaviors of auxetic structures can be developed for other auxetic patterns, such as honeycomb, chiral and re-entrant ones.</p>