The study of r-harmonic maps was proposed by Eells-Sampson in 1965 andby Eells-Lemaire in 1983. These maps are a natural generalization of harmonic maps and are defined as the critical points of the r-energy functional E r (ϕ) = (1/2) M |(d * +d) r (ϕ)| 2 dv M , where ϕ : M → N denotes a smooth map between two Riemannian manifolds. If an rharmonic map ϕ : M → N is an isometric immersion and it is not minimal, then we say that ϕ(M ) is a proper r-harmonic submanifold of N . In this paper we prove the existence of several new, proper r-harmonic submanifolds into ellipsoids and rotation hypersurfaces.