Within this talk, we consider the dimension-reduction procedure in the membrane regime in order to obtain thin-film models of elastic solids. One of the crucial requirements on such models is that penetration of matter is prohibited. While in the bulk this translates to injectivity of deformations, in the film this is no longer true because a thin film can be folded.Thus, we introduce suitable conditions on thin-film deformations that characterize non-interpenetration and show these conditions are enforced by thin-film $\Gamma$-limits of bulk energies assuring injectivity. This is joint work with Martin Kružík (Prague).