A reduced dispersion relation for multibeam laser-plasma instability is derived. The dispersion relation includes combined effects of self-coupling, interaction with other beams by sharing a common scattered light (SL modes), and by sharing a common plasma wave (SP modes). The latters are two most prominent collective effects of all. We have solved the dispersion relation numerically for stimulated Raman scattering, and set different beam configurations and polarizations to discuss the spatial distributions of the temporal growth rate. The instability in the beam overlapping region is complicated, but there are still a few simple rules that govern the system, such as the dominancy of SL modes and subdominancy of backscatter and SP modes. The maximum growth rate always occurs at these special modes, or new mode combined by two or three of special modes. The reduced model provide us the ability to understand the underlying physics of multibeam instabilities under general laser and plasma conditions.

laser-plasma instability,Stimulated Raman scattering (SRS),Stimulated Brillouin scattering