This paper examines session variability modelling for face authentication using Gaussian mixture models. Session variability modelling aims to explicitly model and suppress detrimental within-class (inter-session) variation. We examine two techniques to do this, inter-session variability modelling (ISV) and joint factor analysis (JFA), which were initially developed for speaker authentication. We present a self-contained description of these two techniques and demonstrate that they can be successfully applied to face authentication. In particular, we show that using ISV leads to significant error rate reductions of, on average, 22% on the challenging and publicly-available databases SCface, BANCA, MOBIO, and Multi-PIE. Finally, we show that a limitation of both ISV and JFA for face authentication is that the session variability model captures and suppresses a significant portion of between-class variation.