At the Paul Scherrer Institute (PSI), a methodology titled PSI-NUSS is under development for the propagation of nuclear data uncertainties into Criticality Safety Evaluation (CSE) with the Monte Carlo code MCNPX. The primary purpose is to provide a complementary option for the uncertainty assessment related to nuclear data, versus the traditional approach which relies on estimating biases/uncertainties based on validation studies against representative critical benchmark experiments. In the present paper, the PSI-NUSS methodology is applied to quantify nuclear data uncertainties for the OECD/NEA UACSA Exercise Phase I benchmark. One underlying reason is that PSI's CSE methodology developed so far and previously applied for this benchmark was based on using a more conventional approach, involving engineering guesses in order to estimate uncertainties in the calculated effective multiplication factor (k(eff)). Therefore, as the PSI-NUSS methodology aims precisely at integrating a more rigorous treatment of the specific type of uncertainties from nuclear data for CSE, its application to the UACSA is conducted here: nuclear data related uncertainty component is estimated and compared to results obtained by other participants using different codes/libraries and methodologies.