Recently, an efficient and practical method has been developed for the generation of univariate non-Gaussian wind pressure time histories on low building roofs; this methodology requires intermittent exponential random numbers for the simulation. On the other hand, the conventional spectral representation scheme with random phase is found suitable for the generation of univariate Gaussian wind pressure time histories on low building roofs; this simulation scheme requires uniform random numbers. The dependency of these simulation methodologies on the random number generator is one of the items affecting the accuracy of the simultion result; therefore, an attempt has been made to investigate the issue. This note presents the observed sensitivity of random number sets in repetitive simulations of Gaussian and non-Gaussian wind pressures.