This paper describes the application of a trilinear parallel factor analysis (PARAFAC) to study systematic error during the multi-element determination of a range of analytes in acid digests of solid samples (tea leaves) by ICP-AES and ICP-MS. The three variables studied were the “number of digestions”, in order to assess the systematic error associated with the sample pre-treatment, and the “number of replicates” and “calibration”, to provide information on the systematic error associated with the analytical determination itself. The elements under study were Co, Cr, Cu, Ni, Pb, Rb and Ti by ICP-MS, and Ba, Ca, Fe, Mg, Mn, Sr and Zn by both ICP-MS and ICP-AES. For some elements flame atomic absorption spectrometry was used for comparative purposes. A Chinese tea certified reference material containing many of the metals above was used in the study. The results obtained were compared to results from ANOVA. It was found that the systematic error, expressed as the sum of squares after PARAFAC, was quite different from the results obtained using ANOVA due to the very different way in which the models are built. The PARAFAC approach is shown to be straightforward to implement and robust.