This study explores methodologies for propagating nuclear data uncertainties in radiation shielding calculations. The work is motivated by the aging of pressurized water reactor vessels, where quantifying uncertainties can contribute to improved risk assessment. In this context, the present analysis serves as a preliminary step toward more complex, application-specific scenarios. Two approaches are considered: first-order second-moment (FOSM) sensitivity analysis and Monte Carlo sampling (MCS), both implemented through MCNP6.3. In the FOSM approach, we examine the use of variance reduction in combination with sensitivity calculations, while the MCS method is optimized to address its higher computational demand. Our analysis revealed discrepancies in certain cases when applying variance reduction with sensitivity calculations, which may compromise its applicability under certain conditions. Conversely, the MCS approach, using Sobol and Latin hypercube sampling with fast Total Monte Carlo or Fast GRS techniques, yielded results comparable to FOSM. These findings suggest that using MCS for propagating nuclear data uncertainties in shielding problems should be feasible, while maintaining computational demand similar to that of traditional first-order methods. Future work will test this approach in more complex, realistic configurations.