For the reliability analysis of rock tunnel stability, considering the difficulty in obtaining the statistical data on rock mass parameters, there is the potential inadequacy when using the probabilistic reliability method; on the other hand, the rock tunnel stability is intimately pertinent to a variety of failure modes, meaning it is necessary to consider the issue on structural system reliability. First, based on the interval theory, the uncertainty parameters were represented by adopting the interval variables. Subsequently, aiming at the coexistence of multiple failure modes in rock tunnel engineering, the concept of structural system reliability was introduced, and then a structural system reliability method to calculate the reliability index and assess the rock tunnel stability based on the non-probabilistic interval theory was established. On this basis, the rationality of the proposed method was verified via the engineering example. Finally, the fluctuation range of the uncertainty parameters was defined to further analyze the influence of different parameters in each failure mode on the corresponding reliability index and the system reliability index. The results show that the non-probabilistic reliability index of each failure mode decreases with the increase of the range of interval variables, and the same parameter in various failure modes causes different effects. In addition, the change of uncertainty parameters also leads to the variations in the main failure modes that affect the structural system stability of rock tunnel.