Abstract A growing number of empirical studies have quantified the degree to which evolution is geometrically parallel, by estimating and interpreting pairwise angles between evolutionary change vectors in multiple replicate lineages. Similar comparisons, of distance in trait space, are used to assess the degree of convergence. These approaches amount to element-by-element interpretation of distance matrices, and can fail to capture the true extent of multivariate parallelism when evolution involves multiple traits sampled across multiple lineages. We suggest an alternative set of approaches, co-opted from evolutionary quantitative genetics, involving eigen analysis and comparison of among-lineage covariance matrices. Such approaches not only allow the full extent of multivariate parallelism to be revealed and interpreted, but also allow for the definition of biologically tenable null hypotheses against which empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the direction of evolutionary change can be captured in just a few dimensions, indicating a greater extent of parallelism than previously appreciated. We suggest that applying such multivariate approaches may often be necessary to fully understand the extent and form of parallel and convergent evolution.