  In a remarkable series of papers, Zlil Sela classified the first-order
theories of free groups and torsion-free hyperbolic groups using geometric
structures he called towers. It was later proved by Chlo\'e Perin that if $H$
is an elementarily embedded subgroup (or elementary submodel) of a torsion-free
hyperbolic group $G$, then $G$ is a tower over $H$. We prove a generalization
of Perin's result to toral relatively hyperbolic groups using JSJ and
shortening techniques.
