Abstract We explore the origin of phase-space substructures revealed by the second Gaia data release in the disc of the Milky Way, such as the ridges in the Vφ-r plane, the undulations in the Vφ-r-Vr space and the streams in the Vφ-Vr plane. We use a collisionless N-body simulation with co-spatial thin and thick discs, along with orbit integration, to study the orbital structure close to the Outer Lindblad Resonance (OLR) of the bar. We find that a prominent, long-lived ridge is formed in the Vφ-r plane due to the OLR which translates to streams in the Vφ-Vr plane and examine which closed periodic and trapped librating orbits are responsible for these features. We find that orbits which carry out small librations around the x1(1) family are preferentially found at negative Vr, giving rise to a ‘horn’-like feature, while orbits with larger libration amplitudes, trapped around the x1(2) and x1(1) families, constitute the positive Vr substructure, i.e. the Hercules-like feature. This changing libration amplitude of orbits will translate to a changing ratio of thin/thick disc stars, which could have implications on the metallicity distribution in this plane. We find that a scenario in which the Sun is placed close to the OLR gives rise to a strong asymmetry in Vr in the Vφ-Vr plane (i.e. Hercules vs. ‘the horn’) and subsequently to undulations in the Vφ-r-Vr space. We also explore a scenario in which the Sun is placed closer to the bar corotation and find that the bar perturbation alone cannot give rise to the these features.