Vibration and noise reduction in structures can significantly enhance dynamic stability. In fact, exploitation of such mechanisms can lead to an improvement of aerodynamic performance in flight motions by aircrafts, hydrodynamic performance in ocean water navigation by ships or floating structures, as well as dynamic behavior of machine structures in production processes and systems. In this paper slip damping with layered viscoelastic beam-plate structures for dissipation of vibration energy in aircraft, hydrodynamic, and machine structures is investigated analytically. For this problem, a boundary value partial differential equation is formulated via contact mechanics. In particular, the effect of interfacial pressure distribution variation at the interface of the layered structures on the energy dissipation and logarithmic damping decrement with such layered structures is analyzed and presented for design applications. This allows for a better understanding of the selection process of viscoelastic damping materials for such structures.