The PARAFAC method of factor analysis was used to investigate patterns of tongue shaping in a corpus of 15 German vowels spoken in 3 consonant contexts by 7 speakers at 2 speech rates, using data from electromagnetic articulography. A two-factor model was extracted, giving a succinct, speaker-independent characterization of the German vowel space and of some important coarticulatory effects on vowel articulation. Moreover, the factors appeared to have a plausible physiological substrate. The PARAFAC model places strong constraints on the form that speaker-specific effects can take, since speaker differences must be captured in a single multiplicative weight per speaker and factor. While these constraints appeared acceptable for modelling vocalic aspects of articulation, more consonantally-related aspects, such as coarticulatory behaviour of the tongue-tip, appeared much more difficult to capture in the PARAFAC framework.