SUMMARY Seismicity rate is sometimes observed to correlate with periodic stress oscillations, such as seasonal changes in hydrological loads, or solid-earth and oceanic tidal stresses. However, seismicity modulation is far from being systematic, often weak and the mechanical control is not yet fully understood. Here, a 3-D interacting fault population loaded by a periodic stress has been studied. For that a new earthquake simulator coupling rate-and-state friction and 3-D quasi-dynamic elasticity has been developed, and used to explore the mechanical conditions leading to seismicity modulation. It is first shown that seismicity modulation is maximized when the amplitude of periodic loading stress approaches aσ, a being the viscous parameter of the rate-and-state friction and σ the normal stress in the earthquake source region. The mode of modulation is frequency dependent: short loading periods lead to a stress control (seismicity rate follows the Coulomb stress) while longer periods lead to stressing rate control (seismicity rate tracks Coulomb stressing rate variations). An analytical expression for the critical period Tc separating the two regimes is derived from Dieterich’s theory, showing a dependence of the transition on Coulomb stress amplitude. Finally, the average seismicity rate either scales exponentially with Coulomb stress (stress control), or linearly with Coulomb stressing rate (stressing rate control), as suggested by Dieterich’s theory. These features indicate that for the range of parameters explored, stress redistribution within the fault population is a second order effect in the seismicity modulation, which is primarily controlled by the properties of remote loading. This paper therefore confirms with numerical simulations the Coulomb stress and stressing rate control of seismicity rate, and the limited importance of stress redistribution in controlling earthquake production anticipated by previous theoretical studies.