This paper presents an uncertainty propagation analysis of viscoelastic sandwich laminated structures using a stochastic collocation method based on Smolyak’s sparse grids approach. Shear deformation in the viscoelastic layers is accurately captured by means of layer-wise plate finite elements. Modal properties are determined by solving nonlinear eigenvalue problems due to the frequency-dependent nature of the considered viscoelastic materials. Variations in material properties and layer thicknesses are both treated in a probabilistic way. The variabilities of natural frequencies and modal loss factors of two different viscoelastic laminated plate structures (plane and cylindrical) are studied. Results show that the present method converges quickly with small sample sizes when compared to the classical Monte-Carlo method. The influence of the variability of several parameters on viscoelastic structure modal properties is commented.