Analyses within the field of GIS are increasingly applying stochastic methods and systems that make use of pseudo-random number generators (PRNGs). Examples include Monte Carlo techniques, dynamic modelling, stochastic simulation, artificial life and simulated data development. PRNGs have inherent biases, and this will in turn bias any analyses using them. Therefore, the validity of stochastic analyses is reliant on the PRNG employed. Despite this, the effect of PRNGs in spatial analyses has never been completely explored, particularly a comparison of different PRNGs. Exacerbating the problem is that GIS articles applying Monte Carlo or other stochastic methods rarely report which PRNG is employed. It thus appears likely that GIS researchers rarely, if ever, check the suitability of the PRNG employed for their analyses or simulations. This paper presents a discussion of some of the characteristics of PRNGs and specific issues from a geospatial standpoint, including a demonstration of the differences in the results of a Monte Carlo analysis obtained using two different PRNGs. It then makes recommendations for the application of PRNGs in spatial analyses, including recommending specific PRNGs that have attributes appropriate for geospatial analysis. The paper concludes with a call for more research into the application of PRNGs to spatial analyses to fully understand the impact of biases, especially before they are routinely used in the wider spatial analysis community.