A shape resonance is a metastable state in which an electron is trapped due to the shape of a potential barrier.
Altunata describes a state as being a shape resonance if, "the internal state of the system remains unchanged upon disintegration of the quasi-bound level."
A more general discussion of resonances and their taxonomies in molecular system can be found in the review article by Schulz,; for the discovery of the Fano resonance  line-shape and for the Majorana pioneering work in this field by Antonio Bianconi; and for  
a mathematical review by Combes et al.