The parametric dynamic stability of a pinned-pinned asymmetric sandwich beam resting on a Pasternak foundation with viscoelastic core, subjected to an axial pulsating load is investigated. The effects of thickness ratio of two elastic layers (h31), elastic modulus ratio(E3/E1), the ratio of modulus of the shear layer of Pasternak foundation to the Youngs modulus of elastic layer (Gs/E1), the ratio of length of the beam to the thickness of the elastic layer (lh1), the ratio of in phase shear modulus of the viscoelastic core to the Youngs modulus of the elastic layer (G2/E1), the ratio of thickness of Pasternak foundation to the length of beam (δ/l), coreloss factor (η) the ratio of thickness of viscoelastic layer to that of elastic layer (h21) on the non-dimensional static buckling load are considered. In addition to these the effects of the above parameters on the regions of parametric instability have been studied.