  The exact two-particle energy eigenstates in an asymmetric rectangular box
with periodic boundary conditions in all three directions are studied. Their
relation with the elastic scattering phases of the two particles in the
continuum are obtained. These results can be viewed as a generalization of the
corresponding formulae in a cubic box obtained by L\"uscher before. In
particular, the s-wave scattering length is related to the energy shift in the
finite box. Possible applications of these formulae are also discussed.
