Higher-order tensor data analysis has been extensively employed to understand complicated data, such as multi-way GC-MS data in untargeted/targeted analysis. However, the analysis can be complicated when one of the modes shifts e.g., the elution profiles of specific compounds often with respect to retention time; something which violates the assumptions of more traditional models. In this paper, we introduce a new analysis method named PARASIAS for analyzing shifted higher-order tensor data by combining spectral transformation and the simple PARAFAC modeling. The proposed method is validated by applications on both simulated and real multi-way datasets. Compared to the state-of-art PARAFAC2 model, the results indicate that fitting of PARASIAS is 13 times faster on simulated datasets and more than eight times faster on average on the real datasets studied. PARASIAS has significant advantages in terms of model simplicity, convergence speed, the robustness to shift changes in the data, the ability to impose non-negativity constraint on the shift mode and the possibility of easily extending to data with multiple shift modes. However, the resolved profiles of PARASIAS model are always a little worse when the number of components in the data are larger than three and without using additional factors in PARASIAS model. In such cases, more components are necessary for PARASIAS to model the data than that would be needed e.g., by PARAFAC2. The reason for this is also discussed in this work.