The Laptev Sea Rift in the East Siberian continental margin plays an important role in the geodynamic models for the opening of the Eurasia Basin. The active Gakkel Ridge, which also represents the boundary between the North America and Eurasia plates, abruptly meets the continental margin of the Laptev Sea. On the continental shelf in the prolongation of the Gakkel Ridge, a rift developed since the Late Cretaceous/Early Cenozoic with the formation of five roughly north-south trending depocenters. To better understand the evolution of this rift, a basin modeling study was carried out with PetroMod® software. The modeled sections used in this study were developed on the basis of depth-converted reflection seismic sections. The sections cover the Anisin Basin in the north and the southeastern margin of the Ust´ Lena Rift in the south. The numerical simulations are supported by tectonic and sedimentological field data that were collected in outcrops during the CASE 13 expedition to the New Siberian Islands in 2011. For the Anisin Basin different scenarios were modeled with rift onsets between 110 Ma and 66 Ma. The results show that the present-day temperature field in the area of the Anisin Basin and at the southeastern margin of the Ust´ Lena Rift is characterized by horizontal, seafloor-parallel isotherms. Geohistory curves extracted from the 2D simulations indicate a twofold rift evolution with a stronger initial subsidence in the Late Cretaceous to Early Paleogene and a moderate subsidence in Late Paleogene and Neogene times. Based on the modeling results, an early rift onset around 110 Ma seems to be more realistic than a later one around 66 Ma.