Polymeric materials such as epoxy are widely used as coating layers for the containment building of the nuclear power plant. These layers may be damaged through a hygrothermal process and residual stresses can reach significant levels near the free edges, possibly leading to interface debonding or delamination. Interfacial stress singularities induced in a laminate model consisting of the epoxy coating layer and the concrete substrate is investigated using the time-domain boundary element method. The epoxy layer is assumed to be a linear viscoelastic material and moisture effects are assumed to be analogous to thermal effects. The overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed.