Monte Carlo simulation requires a pseudo‐random number generator with good statistical properties. Linear congruential generators (LCGs) are the most popular and well‐studied computer method for generating pseudo‐random numbers used in Monte Carlo studies. High quality LCGs are available with sufficient statistical quality to satisfy all but the most demanding needs of risk assessors. However, because of the discrete, deterministic nature of LCGs, it is important to evaluate the randomness and uniformity of the specific pseudo‐random number subsequences used in important risk assessments. Recommended statistical tests for uniformity and randomness include the Kolmogorov‐Smirnov test, extreme values test, and the runs test, including runs above and runs below the mean tests. Risk assessors should evaluate the stability of their risk model's output statistics, paying particular attention to instabilities in the mean and variance. When instabilities in the mean and variance are observed, more stable statistics, e.g., percentiles, should be reported. Analyses should be repeated using several non‐overlapping pseudo‐random number subsequences. More simulations than those traditionally used are also recommended for