—We discuss the structure of the Earth’s crust the seismic stratigraphy, thermal evolution, and stretching of the lithosphere in the sedimentary basin of the Cooperation Sea located on the continental margin of Antarctica in the south of the Indian Ocean. The sedimentary basin includes intracontinental and marginal rifts; the former is located on the shelf, and the latter, in the deep-water area. A seismostratigraphic analysis has revealed four sequences in the sedimentary cover of the intracontinental rift, which formed from middle Permian to late Cenozoic, and nine sequences in the sedimentary cover of the marginal rift, which have been deposited since the Middle Jurassic. One-dimensional numerical modeling of the thermal regime and the basement subsidence was performed over 18 points along the profile crossing the basin from the shelf to the lower continental rise. Based on the results of modeling and seismostratigraphic analysis, we have established variations in rock temperature with depth and in the degree of lithosphere stretching throughout the basin rift history. The modeling showed that the depth of the basement subsidence and the thickness of the crystalline part of the basin crust are governed by the lithosphere stretching before sedimentation. The maximum stretching is reached at the depocenters of rift structures (where the crust is the thinnest), being 2.8 before sedimentation and 1.16 after it in the intracontinental rift and 4.6 and 1.4, respectively, in the marginal rift.