This paper presents a new, axiomatic approach to information flow in sequential and parallel programs. Flow axioms that capture the information flow semantics of a variety of statements are given and used to construct program flow proofs. The method is illustrated by a variety of examples. The applications of flow proofs to certifying information flow policies and solving the confinement problem are considered. It is also shown that flow axioms and correctness axioms can be combined to form an even more powerful proof system. Keywords and Phrases: information flow, information security, security certification, parallel programs, axiomatic logic, proof rules.