Purpose <p>In the current study, the dynamic investigation was carried out to determine the displacement of a simply-supported cylindrical shape memory polymer (SMP) sector subjected to the initial conditions due to wind load.</p> Methods <p>The equations of motion in terms of time were derived based on the first-order shear deformation theory (FSDT), the time-dependent behavior of SMP, and Hamilton’s principle. It was observed that there are tenth-order differential equations for the displacement components in terms of time. The theoretical solution was carried out to solve the equations and the displacement components were derived in terms of time. The theoretical results were compared to those obtained by the finite difference method based on the Runge–Kutta fourth-order method.</p> Results <p>There is a very good agreement between numerical and theoretical results. Furthermore, the effects of the radius, thickness, length, and sector angle, the mechanical properties of the shape memory polymer, and the pressure of the wind on the variation of the shell displacement in terms of time were calculated.</p> Conclusion <p>The results indicated that to reduce the deflection of the SMP sector, it is necessary to design a sector with a large thickness and curvature, and at the same time a small length and sector angle. Furthermore, the results showed that to reduce the deflection of the SMP sector, it is essential to choose a shape-memory material with a higher elastic modulus, Poisson’s ratio, and viscosity, and at the same time a lower value of the retardation time and density.</p>