Mega wedges represent adverse conditions during the excavation work of large underground caverns for storing hydrocarbons. Even in “Very Good” rock (assessed using an empirical approach such as the Q system or the RMR), the potentiality of wedges involving atop heading and one or several benches is a recurrent problem that cannot be neglected in unlined rock caverns, only stabilized using rock bolts. The empirical approaches have not been developed to define the necessary support in this very specific context which requires detecting and stabilizing such very large wedges (mega wedges)using a deterministic approach, based on structural geology. Although minimization of the risk and impact of mega wedges is considered by the cavern basic design and the adaptation of the layout and support, a deterministic re-assessment of the areas where mega wedges may occur shall be done during the excavation phase at a more precise scale, on realistic structural conditions. Established on real cases in granite, this paper presents a practical and balanced methodology that is used from the design to the excavation and support phases. For that, as a first step, structural geology aims at identifying location, geometry and potentiality of mega wedges and then rock mechanics helps to characterize the shearing capability of the identified mega wedge and its putative failure. In addition to the support recommendation, the phasing of the support installation with respect to the excavation work to achieve stable condition of the mega wedges is discussed. Results are promising in term of applicability, even if a better estimation of the shear strength parameters of the discontinuities involved in the failure mechanism can be necessary for local fine tuning.