Shape properties of generalized manifolds are considered. Let G be a coefficient domain such that the Alexander-Čech homology with coefficients in G is exact. Let M be a compact n-dimensional generalized manifold over G and \(f: M\to X\) a map onto a finite dimensional compactum X. If either one of the following conditions is satisfied 1) f is shape fibration and strong shape equivalence, 2) f is hereditary shape equivalence, 3) f is a CE-map, then X is an n-dimensional generalized manifold over G.