We investigate the formation of RE galaxies (i.e. of collisional ring galaxies with an empty ring), with N-body/smoothed particle hydrodynamics simulations. The simulations employ a recipe for star formation (SF) and feedback that has been shown to be crucial to produce realistic galaxies in a cosmological context. We show that RE galaxies can form through off-centre collisions (i.e. with a non-zero impact parameter), even for small inclination angles. The ring can be either a complete ring or an arc, depending on the initial conditions (especially on the impact parameter). In our simulations, the nucleus of the target galaxy is displaced from the dynamical centre of the galaxy and is buried within the ring, as a consequence of the off-centre collision. We find that the nucleus is not vertically displaced from the plane of the ring. We study the kinematics of the ring, finding agreement with the predictions by the analytic theory. The SF history of the simulated galaxies indicates that the interaction enhances the SF rate. We compare the results of our simulations with the observations of Arp 147, which is the prototype of RE galaxies.