We study the quantum decay out of the metastable state of a Josephson junction, via tunnelling, in the presence of an external sinusoidal force. We show that the Floquet picture, together with the complex scaling method, provides an adequate nonperturbative method to describe this process. The enhancement of the decay rate near the fundamental resonance assumes a Lorentzian line shape in agreement with recent experiments in the deep quantum regime. Moreover, our results exhibit novel features such as secondary resonances: at higher frequencies, corresponding roughly to a second harmonic induced by the nonlinear potential shape, and at a lower frequency, exactly at half the frequency of the first resonance, revealing a two-photon transition.