In the domain of criticality safety, the efficient propagation of uncertainty in nuclear data to uncertainty in k_eff is an important area of current research. In this paper, a method based on stochastic sampling is presented for uncertainty propagation in MCNPX calculations. To that aim, the nuclear data (i.e. cross sections) are assumed to have a multivariate normal distribution and simple random sampling is performed following this presumed probability distribution. A verification of the developed stochastic sampling procedure with MCNPX is then conducted using the ²³⁹Pu Jezebel experiment as well as the PB-2 BWR and TMI-1 PWR pin cell models from the Uncertainty Analysis in Modeling (UAM) exercises. For the Jezebel case, it is found that the developed stochastic sampling approach predicts similar k_eff uncertainties compared to conventional sensitivity and uncertainty methods. For the UAM models, slightly lower uncertainties are obtained when comparing to existing preliminary results. Further details of these verification studies are discussed and directions for future work are outlined.