Motivation: In the analysis of metabolism using omics data, two distinct and complementary approaches are frequently used: Principal component analysis (PCA) and Stoichiometric flux analysis. PCA is able to capture the main modes of variability in a set of experiments and does not make many prior assumptions about the data, but does not inherently take into account the flux mode structure of metabolism. Stoichiometric flux analysis methods, such as Flux Balance Analysis (FBA) and Elementary Mode Analysis, on the other hand, produce results that are readily interpretable in terms of metabolic flux modes, however, they are not best suited for exploratory analysis on a large set of samples. Results: We propose a new methodology for the analysis of metabolism, called Principal Metabolic Flux Mode Analysis (PMFA), which marries the PCA and Stoichiometric flux analysis approaches in an elegant regularized optimization framework. In short, the method incorporates a variance maximization objective form PCA coupled with a Stoichiometric regularizer, which penalizes projections that are far from any flux modes of the network. For interpretability, we also introduce a sparse variant of PMFA that favours flux modes that contain a small number of reactions. Our experiments demonstrate the versatility and capabilities of our methodology.