The results of a numerical and experimental investigation of the flow structure in symmetric and nonsymmetric flows around V-wings with attached shocks on the leading edges are presented. Emphasis is placed on the appearance of new critical points, including vortex Ferri singularities, in the shock layer and transformations in the flow structure with increase in the angles of attack and yaw. In particular, it is established that the flow structure in the plane of symmetry of the flow around V-wings without yaw, which involves the Mach-type shock configuration, undergoes a jumpwise variation with increase in the angle of attack. Additionally to one Ferri singularity of the node type located at the corner point of the transverse wing contour in the plane of symmetry of the flow, there arise two more critical points, those of flow divergence and convergence. The latter point is the second Ferri singularity; it is located nearer to the bridge-shaped shock of the Mach-type shock system and can be of both the node and the saddle type. In the latter case there appear two vortex Ferri singularities located at the vertices of the contact discontinuities proceeding from this critical point on both sides of the plane of symmetry. Certain data on the position of the critical points relative to the wing contour bend are presented as functions of the wing geometry, together with the transformation of the topological shock-layer flow pattern in the presence of yaw. The comparison of the results calculated within the framework of the Euler model with the experimental data on the shock-layer flow structure obtained using a special optical method for visualizing conical flows showed their good agreement.In Eqs. (1.2) the primes denote the dimensional quantities, while the subscript ∞ refers to the values of the corresponding parameters in the freestream. Here L ′ is the scale length, X = (x, y, z), and V = (u, v, w).