This article provides a comprehensive numerical treatment of a finite crack in an interfacial layer with spatially varying elastic and thermal properties. It is assumed that material properties of the interfacial layer depend only on the coordinate perpendicular to the crack surfaces and vary continuously between those of two dissimilar homogeneous bonding layers. Unlike earlier studies that considered the cracks encountered as open, the current investigation studies cracks in an essentially compressive environment in which the crack faces are in contact and fictional effects play an important role. A finite element model utilizing a recently developed procedure that provides a simple and efficient iterative technique to solve fictional contact problems under small deformations is employed. Numerical examples are provided. Transient and steady-state stress intensity factors (SIFs) are calculated; and the variation in SIF due to change in material properties of the interfacial layer, the length of the crack, and the location of the crack in the interfacial layer is studied.