  L\"uscher established a non-perturbative formula to extract the elastic
scattering phases from two-particle energy spectrum in a torus using lattice
simulations. Rummukainen and Gottlieb further extend it to the moving frame,
which is devoted to the system of two identical particles. In this work, we
generalize Rummukainen-Gottlieb's formula to the generic two-particle system
where two particles are explicitly distinguishable, namely, the masses of the
two particles are different. The finite size formula are achieved for both
$C_{4v}$ and $C_{2v}$ symmetries. Our analytical results will be very helpful
for the study of some resonances, such as kappa, vector kaon, and so on.
