Continental rifting is treated as a mechanical instability developing under horizontal tectonic tension. The instability results in strain localization and the formation of a neck, which is interpreted as a rift zone. At the scale of the whole lithospheric plate, this process occurs in plane-stress conditions and can therefore be modelled to a first approximation by a one-layer plate whose properties represent integral (over thickness) properties of the real lithosphere. We have designed a scaled experimental single-layer lithosphere model having elasto-plastic rheology and lying upon a liquid substratum to study its behaviour under axial horizontal tension. In a homogeneous plate, the instability develops along a linear zone oriented at an angle of ∼60° to the tension axis. This orientation is preserved even when the divergent displacement of the plate boundaries is not plain-parallel but rotational. In the latter case, the strain localization zone is rapidly propagating. When the plate length to width ratio is less than ∼2.5, the necking develops along two branches conjugated at an angle of about 120°, which is frequently observed in actual rift systems. If the model contains a local weak zone (hot spot or fault zone), the rift junction is located at this zone. In the lithospheric models comprising strong (cratonic) and weak segments, strain localization depends on the configuration of the boundary between different lithospheres. The necking starts to form within the weak segment in the vicinity of the cratonic promontories and propagates in opposite directions again at an angle of ca. 60° to the tension axis. In the models containing both a strong lithosphere and local weak zones, the rift configuration depends on their shape and relative positions, with necking always going through the weak zones. In a set of models, we have reproduced the geometry of the boundary between the Siberian craton and the thermally much younger (∼100 Ma) Sayan–Baikal lithosphere in the Baikal rift area. In these models, we were able to obtain the well-known three-branch configuration of the Baikal rift system only by introducing a weak zone in the area of Lake Baikal. Such a zone simulates the Paleozoic suture existing in this area. As in nature, two wide outer branches (eastern and western) are oblique to the regional tension axis, whereas the central one is narrow and orthogonal to the tension direction. In nature and in the model, rifting starts in the central branch corresponding to Lake Baikal. The modelling also predicts the formation of a fourth oblique ∼NS-trending branch to the south of Baikal. Although poorly expressed in the field, this branch has some seismotectonic and magmatic manifestations. The orientations of all four branches with respect to each other and with respect to the regional tension direction are remarkably similar in nature and in the model.