Presently active European Alpine collision has a history of more than 100 Myr convergence. We investigate the collisional contact problem of an apparently rigid African promontory (currently the Italy/Adria block (IAB)) steadily penetrating at 1 cm/yr, over at least the past 45 Myr, into the deformable European plate. We assume that neither continental subduction nor delamination occurs presently in the 300-km-wide contact zone enabling use of the indenter-indentee approach. A key parameter is the aspect ratio h/a, defined by the width of the deformable foreland over the width of the indenter itself. This parameter controls the activation of two fundamentally different modes of deformation: (1) classical indentation mode for h/a>4.4, described by previous authors, and having effect only in a portion of the deformable plate in the vicinity of the indenter and (2) cutting mode for h/a≤4.4 giving plane strain longitudinal splitting of the entire deformable plate and plastic separation of the two halves. We use a matrix operator method to solve for slip lines in the mixed boundary value problem (obliquity, velocity, friction, stress) of the European Alpine case. Implications are as follows: (1) plane stress, vertical lithospheric thickening is the first indentation mode of continental collision; and (2) for the present ratio of h/a≈3 deformation is in the cutting mode and slow plane strain intraplate extension (rifting) is predicted. This mode explains the intraplate stress field obtained from borehole and earthquake data. Considering that the paleoindenter probably has been larger than the IAB it is inferred that h/a has been below 4.4 since at least the end of the Eocene and that consequently the intraplate graben system (Lower Rhine, Rhine, Bresse, Limagne) is due to the cutting of the European plate by Alpine collision.¿ 1997 American Geophysical Union