Determining the chemical rank of multiway data is a key step in many chemometric studies.In this study, a novel method, vector subspace projection with Monte Carlo simulation (VSPMCS), is firstly proposed for three-way data to achieve this goal.This new method estimates an appropriate chemical rank by comparing the projection residuals which are obtained from vector subspace projection analysis of two similar pseudo matrices constructed by the technology of Monte Carlo simulation.The influences of noise, collinearity, non-trilinear contribution, analysis speed and solution on this new method are discussed.Moreover, this new method is compared with other five factor-determining methods, i.e., IND, ADD-ONE-UP, CORCONDIA, LTMC and SPPH, which is present with the aid of two simulation data sets as well as four experimental data sets.The results show a good agreement between simulations and experimentations, suggesting that this new method can accurately and quickly estimate chemical ranks in complicated situations and its precision can be comparable to other five factor-determining methods.