Abstract The method of regularized Stokeslets (MRS) uses a radially symmetric blob function of infinite support to smooth point forces and allows for evaluation of the resulting flow field. This is a common method to study swimmers at zero Reynolds number where the Stokeslet is the fundamental solution corresponding to the kernel of the single layer potential. Simulating the collective motion of N micro-swimmers using the MRS results in at least N 2 pair-wise interactions. Efficient simulation of a large number of swimmers in free space is observed with the implementation of the kernel-independent fast multipole method (FMM) for radial basis functions. We illustrate the complexity of the algorithm on a simple test case where we study regularized point forces, showing that the method is of order N . Additionally, we explore accuracy in time for the MRS where the swimmers are modeled as Kirchhoff rods and the kernel-independent FMM is compared to the direct calculation using the standard MRS. Optimal hydrodynamic efficiency is also explored for different configurations of swimmers.