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• Three-dimensional stability of a non-circular tunnel face is investigated. • The discretization-based failure mechanism is improved to incorporate the soil tension cut-off. • An optimization procedure is presented to solve the critical face pressure. • A practical tunnel project is studied with the proposed approach. In many studies, the face stability evaluations of underground excavations have been performed with an equal-area circular tunnel face instead of the real tunnel shape. This equivalent method greatly facilitates the model construction, but sacrifices the calculation accuracy. To solve this issue, a non-circular tunnel is studied here to assess its face stability by kinematical approach where the discretization-based failure mechanism is used to describe the face failure. In the laboratory tests, it is also found that the soil strength in tensile regime is significantly reduced which is much smaller than the one described by the classical Mohr-Coulomb yield criterion. For this purpose, the tensile strength cut-off is introduced to define a linearly varying soil dilatancy angle with the rotation angle when the tensile stress can be expected in soils. On this basis, the failure mechanism has such a feature that the failure surface in tensile regime is accelerated to bend and eventually forms a rounded corner at the top. The proposed approach is compared with the existing methods in literature and the finite difference method of FLAC3D which proves that the proposed approach has sufficient accuracy and great efficiency. Finally, an engineering example of a tunnel in Hunan Province, China is studied using the proposed approach and some suggestions are given for practical tunnel excavations. [ABSTRACT FROM AUTHOR]