Two-dimensional kinematic modelling of extension based on the numerical solution of the heat transport equation is used to investigate the lateral evolution of lithospheric yield strength during rifting and during postrift relaxation. Two yield strength minima are shown to exist, one beneath the rift centre and the other beneath the undeformed area adjacent to the rift. These are separated by a relative maximum in the transition zone between the rift and the outer area. Initially cold (thick) lithosphere and fast extension give rise to an absolute strength minimum beneath the rift, leading to a narrow rift. On the other hand, initially hot (thin) lithosphere and slow extension lead to an absolute strength minimum beneath the rift sides, which could cause outward migration of the area of principal strain and formation of a wide rift. In contrast to some existing one-dimensional analyses, no lithospheric hardening is necessary for the formation of a wide rift and the conditions for its formation are consequently less restricted. The maximum of strength in the transition zone suggests a third mode of extension characterized by the activation of extension parallel to the rift, with undeformed areas in between. During postrift evolution, the strength of the thinned area progressively increases until the zone adjacent to the rift becomes the weakest area, inducing a widening of the rift in subsequent rifting episodes. The minimum time required for migration of deformation in successive rifting stages is termed the critical relaxation time (CRT) and is shorter for an initially hot lithosphere and low strain rate. CRT values range from few million years to more than 130 Ma for a stretching factor of 1.65. This study highlights major differences with respect to previous one-dimensional analyses when considering lateral heat transport and a progressive crustal and lithospheric thinning from the rift flanks.