Since the late fifties, it has been known that the singularities of Feynman integrals are described by the Landau equations. In this talk, I show that standard Landau analysis can also be generalized to predict where in the final expression for Feynman integrals each singularity can occur, and derive graphical rules for determining when specific sequences of singularities (and thus discontinuities) are allowed. I focus on the example of Feynman diagrams involving all generic masses.