By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams (REGBs) that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle. The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.