Abstract Stress corrosion cracking (SCC) is an important degradation mechanism to be considered for safety assessment of nuclear piping components made of austenitic steels, especially in the heat-affected zones. Damage due to SCC occurs in a susceptible material, in a corrosive environment, in the presence of high temperature and high applied/residual stresses. The operating conditions and the environmental conditions show variations during the lifetime of the power plant. Also, there will be variations in micro-structural properties of the material of piping components. These variations should be taken into account while assessing the safety of the piping component against SCC. This can be accomplished by treating the relevant variables as random or fuzzy depending upon the source and type of uncertainty. In this paper, an attempt has been made to compute the fuzzy failure probabilities of a piping component against SCC with time, using an approach combining the vertex method with the Monte Carlo simulation technique. The initiation and propagation stages of stress corrosion cracks are modelled using a modified PRAISE approach. The degree of sensitisation, material fracture toughness, yield strength, ultimate strength and applied stress are considered as random variables, while operating temperature and oxygen concentration are considered as fuzzy variables. The R6 procedure is used in the computation of the fuzzy failure probabilities. The usefulness of the approach is demonstrated through an example problem.