We present a rheological model of the continental lithosphere during the rift-drift transition, founded on theoretical considerations, numerical modelling, and supported by geophysical and geological evidence from the Red Sea region. The model is based on the fundamental assumption that during the rifting phase the necking lithospheric mantle of the conjugate continental margins retains and accumulates elastic strain. This hypothesis is tested numerically, and thereby it is shown that during the phase of extension the uppermost mantle has the capability to store and maintain recoverable elastic strain over geological times, differently from the upper crust, which exhibits a continuous short-term irreversible deformation by seismic release. After the onset of seafloor spreading, strain recovery and release of the strain energy accumulated in the lithospheric mantle occurs through a phase of non-linear anelastic relaxation. During this phase, the upper crust of the conjugate continental margins experiences post-rift deformation with tectonic inversion of former extensional structures, while the extra space created along the axial zone as a consequence of the rapid contraction of the margins triggers a rapid upwelling of the asthenosphere that induces an initial pulse of fast spreading followed by a steady phase of oceanic crust accretion. We present geophysical evidence supporting this model, including: (1) the observed pattern of oceanic magnetic anomalies in the Red Sea, (2) the distribution of finite crustal strains across the continental margins of Nubia and Arabia, and (3) the distribution of earthquake epicentres along the western margin of the Arabian Plate. We also present new structural data acquired during three geological campaigns performed in 2015 and 2016 along the western Arabian margin, which are consistent with a post-rift phase of compression and inversion of the rift structures. We will also show that a selection of realistic rheological parameters supports non-linear viscoelastic behaviour of the continental lithosphere during the rift-drift transition. Finally, we will show that in the case of the Red Sea ∼40 per cent of the total extensional strain accumulated during the rifting stage has been recovered in the southernmost part of the Arabian margin conjugate to the Nubian Plate (∼19 • N), while this percentage decreases to ∼14 per cent around 23.8 • N, where the continental margin faces the youngest spreading segment, and it is zero north of this area, where the Red Sea is still in the rifting stage. Taking into account of the age of oceanization along the central and northern Red Sea, this implies an average recovery of ∼10 per cent Myr -1 .