The response of solid materials and structures to shock loading is an active research area for studying the prevention and mitigation of shock-induced damages and failures. The tensile stresses generated in the target due to wave interactions have the potential to cause damage to the target. Spallation is a phenomenon where the tension generated by the interaction of release waves surpasses the tensile strength of the material. This excess tension can lead to structural damage and the creation of fragments, often observed at the free end of the material. The aim is to study the damage initiation and evolution in an elastic medium with multiple layers caused due to impact by observing the interaction of waves happening in the layered medium. The waves generated on impact propagate in the impactor-target system and interact with the other waves and the interfaces present in the system. Exact analytical stress and particle velocity expressions are obtained using the mass and momentum balance for all the possible wave interactions occurring in the impactor-target system. The impactor-target system's interactions are all resolved by a computer program that tracks each wave as it travels through the system. Tensile stress can be generated at any place within the layered medium when the two unloading waves interact with each other. Depending on the magnitude of the tensile stress generated due to the interaction of unloading waves and the tensile strength of the material, it is decided whether the tensile stress will lead to complete failure or would damage the layer. A scalar damage state variable is used to represent small-scale material damages that cannot be resolved by the computational grid. The constitutive equation is modified by reducing the Young's modulus linearly. The growth of damage in time is governed by strain-based damage evolution law. Damage initiation and evolution are checked at every point of tensile stress occurrence in the impactor-target system. The study explores tensile stress occurrences, analysing spatial and temporal variations of multiple damage incidents within the layered medium. The impact behaviour of a single-layer and a multi-layered target obtained from the present model, in terms of stress and particle velocity, is verified through Finite Element simulations of the identical impact problems, where the damage evolution criterion is incorporated using a VUMAT subroutine.