<p>The nonlinear dynamic problem of an incompressible viscoelastic composite spherical shell under sudden constant loading on its inner and outer surfaces was studied. A mathematical model was established in this paper. Starting from the fundamental equations, the viscoelastic constitutive equation was expressed in the form of Stieltjes convolution. The governing equations for the displacement function were derived, and general solutions for displacement and stress expressions in the Laplace domain were obtained using Laplace transforms. The displacement and stress distributions were then solved via inverse Laplace transforms. Additionally, the variation rules of stress and displacement inside the spherical shell with increasing internal/external pressures and geometric parameters of the composite shell were discussed.</p>