An analytical expression is derived for the time-averaged radiation force induced by an acoustic wave field between N particles freely suspended in a fluid. Both the host fluid and the medium inside the particles are assumed to be ideal compressible fluids. The incident field is assumed to be moderate so that the scattered and refracted fields of the particles can be taken to linear approximation. Multiple re-scattering of sound between the particles and shape modes of all orders are allowed for. No restrictions are imposed on the size of the particles, the separation distances between them and their number. The present study substantially extends the existing theory, which is based on essential simplifications and valid only for pairwise interactions. In particular, the new theory allows one to follow continuously the evolution of the radiation interaction force from large to small separation distances. The general results are illustrated in the case of two air bubbles in water. It is shown that generally the interbubble force behaves in far more complicated way than is predicted by the classical Bjerknes theory.