<p>The influence of the Winkler elastic foundation on the dynamics of three-layer conical shells with a discretely inhomogeneous lightweight rib-reinforced core under impulse load has been analyzed for various boundary conditions. In the lightweight core, the rib spacing greatly exceeds the rib cross-sectional dimensions; therefore, the theory of independent static and kinematic hypotheses for each layer has been applied. Based on the Hamilton–Ostrogradsky variational principle, the equations of motion and the natural boundary and initial conditions for the three-layer conical shell on the Winkler elastic foundation have been derived using the Timoshenko shell-and-beam theory. This approach has made it possible to construct a physically consistent finite element model for the three-layer conical shells composed of different materials and to obtain numerical results describing the dynamic response of the structure resting on the elastic foundation. Through specific examples, the study has analyzed the influence of geometric parameters, taper angle, boundary conditions, and elastic-medium stiffness on the dynamics and natural frequencies of the three-layer conical structure subjected to impulse load. New mechanical effects have been established.</p>