Stress corrosion cracking (SCC) is an important degradation mechanism to be considered for failure assessment of nuclear piping components made of austenitic steels. In this paper, an attempt has been made to compute the failure probabilities of a piping component against SCC with time using Monte Carlo simulation (MCS) technique. The initiation and propagation stages of stress corrosion cracks are modelled using the general methodology recommended in PRAISE modified by using the recommendations given by ASM for more rational modelling of stress field around cracks for estimating their growth with time. Degree of sensitization, applied stress, time to initiation of SCC, initial crack length, and initiation crack growth velocity are considered as random variables. An attempt has been made to study the stochastic propagation of stress corrosion cracks with time, using MCS technique. The trend of the distribution of crack depths at the initial stages obtained from simulation are compared and is found to be in satisfactory agreement with the relevant experimental observations reported in the literature. The failure probabilities are computed using two different failure criteria, namely (a) based on net-section stress and detectable leak rate as recommended in PRAISE and (b) based on R6 approach (using R6-option 1 curve as the failure assessment diagram). The procedure presented in the paper is general and the usefulness of the same is demonstrated through an example problem.