  A proposal by L\"uscher enables one to compute the scattering phases of
elastic two-body systems from the energy levels of the lattice Hamiltonian in a
finite volume. In this work we generalize the formalism to S--, P-- and D--wave
meson and baryon resonances, and general total momenta. Employing nonvanishing
momenta has several advantages, among them making a wider range of energy
levels accessible on a single lattice volume and shifting the level crossing to
smaller values of $m_\pi L$.
