We construct a refined two-dimensional mathematical model for dynamic deformation process of tree-layer plates and shells having transversally soft filler. The model is based on the classical Kirhhoff-Love model for inner layers and a hypothesis proposed in the present paper. This hypothesis states that laws of variation of displacements through the thickness of filler are similar to each other both under static and dynamic loadings. We present a simplified version of quasi-static equations of two-dimensional theory of elasticity for transversally soft filler that can be integrated through the transversal coordinate. We introduce two two-dimensional unknown functions, namely, transversal tangent stresses that are constant through the thickness. Using these functions, we can describe a stress-strain state of plates and shells under consideration. We use the generalized Ostrogradskii-Hamilton variational principle for describing dynamic processes of deformation of plates and shells with large variability of stress-strain characteristics. As a result, we obtain two-dimensional general equations of motion such that the inertial terms are of the same degree of accurateness compared to the other terms. We present the results of simplification of these equations for the case of small variability of stress and strain parameters.