Abstract—This paper is concerned with the free vibration analysis of viscoelastic thin plates of uniformly varying cross-section constituted with four-parameter model under different time-dependent loadings. Mixed finite element formulation in Laplace-Carson domain is used to construct a functional for the analysis of the viscoelastic plate of uniformly varying cross-section. Four-parameter model is taken into consideration in viscoelastic modeling. Durbin inverse Laplace transform technique is utilized to obtain the viscoelastic solution in time-domain. The developed solution technique is applied to several dynamic example problems to analyze the free vibration behavior of viscoelastic plates of uniformly varying cross-section.