ABSTRACT We present 3D hydrodynamic models of the interaction between the outflows of evolved, pulsating, Asymptotic Giant Branch (AGB) stars and nearby (<3 stellar radii) substellar companions (Mcomp ≲ 40 MJ). Our models show that due to resonances between the orbital period of the companion and the pulsation period of the AGB star, multiple spiral structures can form; the shocks driven by the pulsations are enhanced periodically in different regions as they encounter the denser material created by the substellar companion’s wake. We discuss the properties of these spiral structures and the effect of the companion parameters on them. We also demonstrate that the gravitational potential of the nearby companion enhances the mass-loss from the AGB star. For more massive (Mcomp > 40 MJ) and more distant companions (>4 stellar radii), a single spiral arm forms. We discuss the possibility of observing these structures with the new generations of high-resolution, high-sensitivity instruments, and using them to ‘find’ substellar companions around bright, evolved stars. Our results also highlight possible structures that could form in our Solar system when the Sun turns into an AGB star.