Since the pioneer studies of Trueman and others in the 1920s, some palaeontologists have used a considerable variety of statistical techniques to describe and analyse individuals and associations of fossil taxa. The increasing sophistication of the algorithms used partly reflects advancing technology from long-hand calculations to computer-based analyses. A progression from univariate graphical and statistical techniques through bivariate analysis to the more sophisticated multivariate analyses can be illustrated by reference to a series of classic case histories on a wide variety of fossil organisms. Nevertheless, despite the necessity for the accurate description of fossils and fossil assemblages and a framework within which to test hypotheses, statistical analysis in palaeontology is far from routine. Access to powerful microcomputers is now widespread amongst palaeontologists but there is a shortage of specialist software packages designed to meet their needs. The PALSTAT package is one of a number of attempts, using the many advantages of the microcomputer, to provide a centralized system of routine graphical and statistical techniques within an investigative framework. The strategy is illustrated with two case histories.