Results of modeling of the formation of the Vilyui sedimentary basin are presented. We combine backstripping reconstructions of sedimentation and thermal regime during the subsidence with a numerical simulation based on the deformable solid mechanics. Lithological data and stratigraphic sections were used to “strip” the sedimentary beds successively and calculate the depth of the stratigraphic units during the sedimentation. It is the first time that the evolution of sedimentation which is nonuniform over the basin area has been analyzed for the Vilyui basin. The rift origin of the basin is proven. We estimate the spatial distribution of the parameters of crustal and mantle-lithosphere extension as well as expansion due to dike intrusion. According to the reconstructions, the type of subsidence curves for the sedimentary rocks of the basin depends on the tectonic regime of sedimentation in individual basins. The backstripping analysis revealed two stages of extension (sediments 4–5 km thick) and a foreland stage (sediments > 2 km thick). With the two-layered lithosphere model, we conclude that the subcrustal layer underwent predominant extension (by a factor of 1.2–2.0 vs. 1.1–1.4 in the crust). The goal of numerical experiments is to demonstrate that deep troughs can form in the continental crust under its finite extension. Unlike the oceanic rifting models, this modeling shows no complete destruction or rupture of the continental crust during the extension. The 2D numerical simulation shows the possibility of considerable basement subsidence near the central axis and explains why mafic dikes are concentrated on the basin periphery.