Commonly, Finite Element (FE) analyses of mechanised tunnel excavation are performed using a step-by-step approach, in which a slice of soil elements is removed at each analysis step, representing the soil excavated during the advance phase of the TBM, and a fixed face support pressure is applied at the tunnel face. The complex interactions between the TBM (Tunnel Boring Machine) and the surrounding soil are simulated in a very simplified manner by applying fictitious perturbations at the excavation boundary. Those perturbations are calibrated in order to get realistic displacements in greenfield conditions, usually in terms of expected volume loss and shape of the surface transverse settlement trough. In this paper, it is suggested to simulate the advancement phase of the TBM as a continuous process using a Eulerian approach, without introducing aprioristic assumptions on the expected volume loss. The analysis is carried out in a frame of reference fixed on the shield; soil material can flow into and out of the FE mesh through the boundaries of the examined control volume. The pressure bulkhead also constitutes an outflow boundary; by controlling the rate of soil extracted from the latter, different face support pressure can be achieved, leading to different results in terms of volume loss. Either the Arbitrary Lagrangian Eulerian (ALE [1]) or the Coupled Eulerian Lagrangian method (CEL, [2]) are used to solve the problem. Results of a small scale test devised at the ENTPE Lyon [3] are used as a reference to assess the performance of the proposed method. Due to high computational cost of the simulations, some parametric analyses are performed in plane strain conditions, for a longitudinal section of the small scale model. This research has been partly funded by the European Commission through the FP7 cooperative project NeTTUN: New Technologies for Tunnelling and UNderground works