The dynamic processes leading to synconvergent exhumation of high-pressure low-temperature (HP-LT) rocks at oceanic accretionary margins, as well as the mechanisms maintaining nearly steady state regime in most accretion prisms, remain poorly understood. The present study aims at getting better constraints on the rheology, thermal conductivity, and chemical properties of the sediments in subduction zones. To reach that goal, oceanic subduction is modeled using a forward visco-elasto-plastic thermomechanical code (PARA(O)VOZ-FLAC algorithm), and synthetic pressure-temperature-time (P-T-t) paths, predicted from numerical experiments, are compared with natural P-T-t paths. The study is focused on the well constrained Schistes Lustrés complex (SL: western Alps) which is thought to represent the fossil accretionary wedge of the Liguro-Piemontese Ocean. For convergence rates comparable to Alpine subduction rates (∼3 cm yr−1), the best-fitting results are obtained for high-viscosity, low-density wedge sediments and/or a strong lower continental crust. After a transition period of 3–5 Ma the modeled accretionary wedges reach a steady state which lasts over 20 Ma. Over that time span a significant proportion (∼35%) of sediments entering the wedge undergoes P-T conditions typical of the SL complex (∼15–20 kbar; 350–450°C) with similar P-T loops. Computed exhumation rates (<6 mm yr−1) are in agreement with observations (1–5 mm yr−1). In presence of a serpentinite layer below the oceanic crust, exhumation of oceanic material takes place at rates approaching 3 mm yr−1. In all experiments the total pressure in the accretionary wedge never deviated by more than ±10% from the lithostatic component.