A tough thermoplastic polymer may show a transition to brittle behaviour when a skin of different properties forms on, or is painted or bonded onto, its free surfaces. A small-scale yielding, linear elastic analysis of the core material, in combination with an axisymmetric plate analysis of the skin, is used here to explore the role in this phenomenon of skin core modulus inequality. When applied to the homogeneous (equal modulus) case, this very simple constraint model appears to provide independent support for the ASTM thickness criterion for plane-strain LEFM test validity. When applied to previously published impact fracture data from inhomogeneous (polyethylene–polypropylene) sandwich plates, the model successfully explains the shift in brittle–tough transition temperature precipitated by bonding a polypropylene skin to a polyethylene core. The model offers specific predictions for the effect, on transition temperature shift, of variables such as skin thickness and core properties; these predictions remain to be verified.