Masonry tunnels are underground structures which can experience degradation due to ageing resulting in damage or cracking. In this work, the stability of these structures is studied using the upper-bound kinematic approach of yield design theory. This method allows estimating the ultimate load of any system knowing the geometry and the strength of its constitutive materials. However, the determination of the optimal failure mechanism, that is to say the one giving the upper-bound of the ultimate load, can be tricky as regards the interactions between the ground and the structure itself. To overcome this issue, it has been chosen to decompose the problem in two sub-problems. On the one hand, existing kinematic models dealing with the stability of excavations are extended to cohesive-frictional grounds. On the other hand, a mechanism representing the deformation observed on-field is explored to assess the masonry lining stability. Yield design theory is used to determine upper-bound estimations of the ultimate load for excavations in purely frictional grounds, cohesive-frictional grounds, and for a masonry vault subjected to a concentrated load.