The frictionless contact problem for a layered composite which consists of two elastic layers having different elastic constants and heights resting on two simple supports is considered. The external load is applied to the layered composite through a rigid stamp. For values of the resultant compressive force P acting on the stamp vertically which are less than a critical value $P_{cr}$ and for small flexibility of the layered composite, the continuous contact along the layer - the layer and the stamp - the layered composite is maintained. However, if the flexibility of the layered composite increases and if tensile tractions are not allowed on the interface, for P > $P_{cr}$, a separation may be occurred between the stamp and the layered composite or two elastic layers interface along a certain finite region. The problem is formulated and solved for both cases by using Theory of Elasticity and Integral Transform Technique. Numerical results for $P_{cr}$, separation initiation distance, contact stresses, distances determining the separation area, and the vertical displacement in the separation zone between two elastic layers are given.