The Alps are one of the best studied orogens, but arguably also one of the most disputed ones. Several major geodynamic processes remain unclear, such as the mechanism of (U)HP rock exhumation, for example exhumation during plate divergence or syn-convergent exhumation, or the mechanism of subduction initiation, for example vertically forced initiation by gravitational sinking or horizontally forced initiation due to plate convergence. The Tibetan plateau is currently the highest continental plateau and its first-order geometry is well constrained. Spatial variations in topography and crustal thickness can be used to estimate horizontal forces per unit length from spatial variations in gravitational potential energy per unit area. Knowledge of forces and stresses is essential to understand geodynamic processes. However, maximal magnitudes of differential stresses occuring locally within the crust remain disputed and range from ca. 10 MPa to several hundreds of MPa. Deterministic mathematical modelling based on the fundamental laws of physics is one method to test different geodynamic hypotheses and quantify potential stress magnitudes. Here, we employ 2D petrological-thermo-mechanical numerical simulations to the Alpine orogeny to test the two hypotheses of horizontally forced subduction initiation and syn-convergent exhumation with a single simulation and with petrological and geochronological data. We use 3D mechanical numerical calculations for the Tibetan plateau, to quantify the impact of (i) a realistic double curvature of the Earth’s crust, (ii) the effective viscosity of the crust, (iii) the stress exponent of a power-law flow law and (iv) the plateau’s corner regions on the 3D crustal stress field.