A factor-analytic model, PARAFAC, has been shown to yield highly significant and interpretable results when applied to the analysis of tongue shapes in particular languages. However, the forms of the solutions differ from language to language. A conceptual model that provides an account for cross-language variability in terms of coordinative structures that may vary in a language-specific manner is developed. This model rationalizes both the success of the PARAFAC procedure within languages and the poor cross-language replicability of PARAFAC solutions. We consider methods for quantitatively comparing the results of PARAFAC analyses of data from different languages using data from Icelandic and English as a test case. A cross-language factor solution that accounts for 90% of the variance in tongue position measurements is presented and interpreted in terms of the conceptual model.