We consider the solvability of a hybrid model for the vibration of a vertical slender structure mounted on an elastic seating. The slender structure is modeled as a Rayleigh beam and gravity is taken into account. The seating and foundation block are modeled as rigid bodies connected by elastic springs with damping mechanisms. We show how an existence result for a general linear vibration problem in variational form may be applied to the weak variational problem for this system.