Based on a thorough analysis of known rheological models used to describe the behavior of continuous media, it has been concluded that the Kelvin viscoelastic medium model is the most appropriate for modelling the properties of metallic powder subjected to vibrational compaction. This model enables the study of wave propagation in a medium with internal friction (viscosity). The rheological model consists of multiple blocks, each incorporating elastically and viscously arranged elements in a characteristic configuration. A wave equation describing the propagation of deformation waves in the compacted layer of metallic powder, treated as a system with distributed parameters, is presented for the Kelvin viscoelastic medium model. Numerical values of experimental coefficients have been determined, allowing for a sufficiently accurate estimation of the dynamic modulus of elastic deformation and the dynamic viscosity coefficient of the metallic powder and surfactant mixture, depending on the powder type and the degree of vibrational compaction. Using the obtained experimental coefficients, graphical dependencies have been constructed to illustrate the variation of the dynamic modulus of elastic deformation as a function of the relative density of the metallic powder. Given the established coefficient values, the discrepancy between theoretical and experimental data for determining the dynamic modulus of elastic deformation does not exceed 4%.