A new method for shift-invariant non-negative tensor factorization is presented for the analysis of GC-MS data. The method is a fast alternative to the Parallel Factor Analysis 2 (PARAFAC2) model, which is used to resolve co-eluting peaks and extract peak areas and clean mass spectra. The new method can also be extended to a more flexible soft-shift invariant tri-linearity algorithm, which potentially can model shifts and shape changes of elution profiles across samples.