Numerical models of rupture dynamics provide great insights into the physics of fault failure. However, resolving stress interactions among multiple faults remains challenging numerically. Here, we derive the elastostatic Green’s functions for stress and displacement caused by arbitrary slip distributions along multiple parallel faults. The equations are derived in the Fourier domain, providing an efficient means to calculate stress interactions with the fast Fourier transform. We demonstrate the relevance of the method for a wide range of applications, by simulating the rupture dynamics of single and multiple parallel faults controlled by a rate‐ and state‐dependent frictional contact, using the spectral boundary integral method and the radiation‐damping approximation. Within the antiplane strain approximation, we show seismic cycle simulations with a power‐law distribution of rupture sizes and, in a different parameter regime, sequences of seismogenic slow‐slip events. Using the in‐plane strain approximation, we simulate the rupture dynamics of a restraining stepover. Finally, we describe cycles of large earthquakes along several parallel strike‐slip faults in three dimensions. The approach is useful to explore the dynamics of interacting or isolated faults with many degrees of freedom.