The stability of the tunnel face has been an important issue investigated by many scholars. To fully study the failure evolution of tunnel face and the hydro-mechanical behavior of surrounding soils in saturated stratum, a two-phase single-point material point method (MPM) considering the fluid–solid coupling effect is adopted to investigate this issue. Firstly, this proposed method is validated by comparing with the results obtained from the existing literatures. Secondly a series of MPM simulations are carried out to study the critical support pressure and failure mechanism of tunnel face in saturated soils. The arching effect range and inclination angle of failure soil in front of tunnel face are analyzed and determined. Finally, the post-failure mechanism of tunnel face is investigated. The run-out distance and the flow-in mass of failed soil in tunnel are calculated through the parametric analysis. The results show that MPM can well predict the whole failure process of tunnel face. The proposed method can provide useful guidance for practical tunnel designs.