  Many low energy hadrons, such as the rho, can be observed as resonances in
scattering experiments. A proposal by L\"uscher enables one to determine
infinite volume elastic scattering phases from the two-particle energy spectrum
measured from finite periodic lattices. In this work, we generalize the
formalism to the case where the total momentum of the particles is non-zero;
i.e. the lattice frame is not the center-of-mass frame of the scattering
particles. There are several advantages to this procedure including making a
wider variety of center of mass energies accessible with a fixed lattice
volume, and making the avoided level crossing in a P-wave decay occur with a
smaller volume. The formalism is tested with a simple lattice model of two
fields with different masses and a 3-point coupling in 3+1 dimensions. We find
remarkable agreement between the rest-frame and non-rest-frame scattering.
