We employ a methodology, based on established approaches for determining the critical thickness for strain relaxation in planar films, to determine critical dimensions for coherently strained coaxial nanowire heterostructures. The model is developed and executed for various specific core-shell heterostructures in [111] zinc blende and [0001] wurtzite geometries. These calculations reveal that critical dimensions in such heterostructures can be quantified by a unique critical core radius and a critical. shell thickness, which is dependent on the core radius. It is anticipated that this work will serve as a guide to determine the feasibility of specific coherently strained nanowire heterostructure designs. (c) 2006 American Vacuum Society.