Membrane budding and wrapping of particles, such as viruses and nano-particles, play a key role in intracellular transport and have been studied for a variety of biological and soft matter systems. We study nano-particle wrapping by numerical minimization of bending, surface tension, and adhesion energies. We calculate deformation and adhesion energies as a function of membrane elastic parameters and adhesion strength to obtain wrapping diagrams. We predict unwrapped, partially wrapped, and completely wrapped states for prolate and oblate ellipsoids with various aspect ratios and particle sizes. In contrast to spherical particles, where partially wrapped states exist only for finite surface tensions, partially wrapped states for ellipsoids occur already for tensionless membranes. In addition, the partially wrapped states are long-lived, because of an increased energy cost for wrapping of the highly curved tips. Our results suggest a lower uptake rate of ellipsoidal particles by cells and thereby a higher virulence of tubular viruses compared with icosahedral viruses, as well as co-operative budding of ellipsoidal particles on membranes.