In this study, a comprehensive analysis about the dynamic response characteristics of visco-elastic plates is given. To construct the functional in the Laplace-Carson domain for the analysis of visco-elastic plates based on the Kirchhoff hypothesis, functional analysis method is employed. By using this new energy functional in the Laplace-Carson domain, moment values that are important for engineers can be obtained directly with excellent accuracy and element equations can be written explicitly. Three-element model is considered for modelling the visco-elastic material behavior. The solutions obtained in the Laplace-Carson domain by utilizing mixed finite element formulation are transformed to the time domain using the Durbin's inverse Laplace transform technique. The proposed mixed finite element formulation is shown to be simple to implement and gives satisfactory results for dynamic response of visco-elastic plates.