<p>Three-dimensional static behavior of cylindrical sandwich panels with a viscoelastic polymer core and functionally graded graphene platelets-reinforced composite (FG-GPLRC) face sheets, subjected to transverse uniform pressure and under various boundary conditions is investigated. For the case of simply supported boundary conditions, an analytical approach using Fourier series expansion in the circumferential and axial directions, combined with the state-space technique in the radial direction, is developed. For other types of boundary conditions, a semi-analytical solution employing the numerical differential quadrature method (DQM) in the circumferential and axial directions, along with the state-space method in the radial direction, is utilized. The governing equations are solved in the Laplace domain, and the obtained results are transformed back to the time domain using a numerical inverse Laplace transform method. Uniform and four types of functionally graded (FG) graphene distributions in the faces are considered. The mechanical properties of the composite face sheets are determined using the Halpin–Tsai model and the rule of mixtures. The time-dependent behavior of the viscoelastic core is modeled according to Boltzmann's superposition principle, and the relaxation modulus is defined using the Prony series based on the generalized Maxwell model. </p><p>A numerical comparison is made with available published results to assess the validity of the present approach. Stress and displacement curves are plotted, and the effects of panel’s geometry, distribution patterns and weight fraction of graphene platelets (GPL) in the face sheets, boundary conditions, and elapsed time since the start of loading are discussed.</p>