The non-singular stress at the tip of an interface crack in a layered structure affects the directional stability of interfacial crack propagation and may favour or hamper kinking and subsequent growth of the crack into one of the layers. In this work we present novel solutions for the T-stress associated to elementary edge-loading modes in homogenous and bimaterial, isotropic, edge cracked layers. Elasticity solutions for equal-thickness layers are derived using the Wiener-Hopf technique, while a semi-analytical approach, based, on the interaction integral technique and recent elasticity solutions for the crack tip compliances, is formulated and also applicable to unequal thickness layers. The solutions have relevant applications, which include the sizing of fracture specimens for the characterization of the interfacial toughness and the implementation into numerical models for the analysis of crack propagation.