In the paper a sandwich plate, of rectangular form, with magnetorheological (MR) fluid core is investigated. The plate consists of two outer layers made of aluminium and an MR fluid layer in between. The plate edges are clamped. It was assumed that the aluminium layers are pure elastic. The energy is dissipated only in the MR fluid layer. Additional assumptions concerning displacements, deformations and stresses are introduced in the calculations. The average power dissipated per unit area of the plate for selected modes of vibrations was determined. A simple method of energy assessment was presented. The results of the calculations can be useful in a semiactive control of continuous systems.