Abstract This paper deals with the dynamic properties of three-layered composite sandwich open circular cylindrical shells (CSOCCS). First, the equations of motion that govern the free vibrations of CSOCCS are derived by applying Hamilton’s principle based on the first-order shear deformation shell theory. Owing to considering the effect of rotary inertias and shear deformation, thin-to-moderately thick shells can be analyzed. Next, these equations are solved by means of the closed-form Navier method. The calculated results are compared with the findings of previous studies and those obtained by the finite element method, and a good agreement is observed. The variation of modal loss factor and frequency with system parameters is evaluated and presented graphically. It is the first time to study the dynamic properties of composite open circular cylindrical shells with constrained viscoelastic core.