We apply the pure shear model of lithospheric extension to rifting on Mars and investigate the range of initial ambient conditions that allow for narrow rifting. The results are applied to the Coracis Fossae, constraining the crustal thickness at the time the rift formed. We thus find that the crustal thickness at 3.5--3.9 Gyr is unlikely to have exceeded ~50 km. This is significantly lower than the estimates for the present day crustal thickness in that region (~70 km) and interpreted as an indication for continued crustal production at that time.