The physical reasons for the diffculty in predicting accurately strong swept-shock-wave/turbulent-boundary-layer interactions are investigated. A well-documented sharp-fin/plate flow has been selected as the main test case for analysis. The selected flow is calculated by applying a version of the Baldwin–Lomax turbulence model, which is known to provide reliable results in flows characterized by the appearance of crossflow vortices. After the validation of the results, by comparison with appropriate experimental data, the test case flow is studied by means of stream surfaces which start at the inflow plane, within the undisturbed boundary layer, and which are initially parallel to the plate. Each of these surfaces has been represented by a number of streamlines. Calculation of the spatial evolution of some selected stream surfaces revealed that the inner layers of the undisturbed boundary layer, which are composed of turbulent air, wind around the core of the vortex. However, the outer layers, which are composed of low-turbulence air, fold over the vortex and at the reattachment region penetrate into the separation bubble forming a low-turbulence tongue, which lies along the plate, underneath the vortex. The conical vortex at its initial stage of development is completely composed of turbulent air, but gradually, as it grows linearly in the flow direction, the low-turbulence tongue is formed. Also the tongue grows in the flow direction and penetrates further into the separation region. When it reaches the expansion region inboard of the primary vortex, the secondary vortex starts to be formed at its tip. Examination of additional test cases indicated that the turbulence level of the elongated tongue decreases if the interaction strength increases. The existence of the low-turbulence tongue in strong swept-shock-wave/turbulent-boundary-layer interactions creates a mixed-type separation bubble: turbulent in the region of the separation line and almost laminar between the secondary vortex and the reattachment line. This type of separation cannot be simulated accurately with the currently used algebraic turbulence models, because the basic relations of these models are based on the physics of two-dimensional flows, whereas in a separation bubble the whole recirculation region is turbulent. For improving the accuracy of the existing algebraic turbulence models in predicting swept-shock-wave/turbulent-boundary-layer interactions, it is necessary to develop new equations for the calculation of the eddy viscosity in the separation region, which will consider the mixed-flow character of the conical vortex.