In this work, we study the face stability of circular tunnels excavated in heavily fractured and ‘low quality’ rock masses that follow the non-linear Hoek–Brown (HB) failure criterion. To that end, the rotational mechanism recently proposed by Mollon et al. [22] has been generalized to consider the non-linearity of the HB failure criterion, so that we can employ ‘instantaneous’ values of cohesion and of friction angle that depend on the stress level, at the same time that we fulfill the assumption of associated flow. To validate the new methodology, we compare our limit analysis results with the results of a 3D finite difference numerical code. Finally, we employ the new improved failure mechanism to develop design charts that can be used to estimate the tunnel face critical pressure, for a wide variety of practical cases, and as a function of the tunnel diameter and of the rock mass parameters.