In this paper, the free vibration and low velocity impact response of a sandwich plate with a Magneto Rheological (MR) flexible core have been studied. The rectangular sandwich plate contains a Magneto Rheological (MR) flexible core and two constrained layers. The MR materials have different properties with respect to different magnetic field intensities. The governing equations of motion have been derived using Hamilton principles. The solution of these equations was obtained using Fourier series and analytical systematic procedure. Using the proposed solution method, the natural frequencies, structural loss factors, impact load and transverse deflection of the plate were calculated. Also, the contact force history was derived using a two degrees of freedom spring mass model analytically. The effects of variations of magnetic field intensity on the natural frequency, loss factors, contact force and deformations of the plate and impactor were investigated. In ordre to calculate the equivalent mass of the plate, the obtained fundamental natural frequency from solution of eigen value problem was used. The obtained equivalent mass of the plate was used in analytical spring mass model. The results show that with systematic variation of magnetic field, the magnitudes of transverse stiffness, structural loss factors and maximum contact force can be changed and controlled, respectively.