In this dissertation, we present LaSCO, the Language for Security Constraints on Objects, a new approach to expressing security policies using policy graphs and present a method for enforcing policies so expressed. Other approaches for stating security policies fall short of what is desirable with respect to either policy clarity, executability, or the precision with which a policy may be expressed. However, LaSCO is designed to have those three desirable properties of a security policy language as well as: relevance for many different systems, statement of policies at an appropriate level of detail, user friendliness for both casual and expert users, and amenability to formal reasoning. In LaSCO, the constraints of a policy are stated as directed graphs annotated with expressions describing the situation under which the policy applies and what the requirement is. LaSCO may be used for such diverse applications as executing programs, file systems, operating systems, distributed systems, and networks. Formal operational semantics have been defined for LaSCO. An architecture for implementing LaSCO on any system, is presented along with an implementation of the system-independent portion in Perl. Using this, we have implemented LaSCO for Java programs, preventing Java programs from violating policy. A GUI to facilitate writing policies is provided. We have studied applying LaSCO to a network as viewed by GrIDS, a distributed intrusion detection system for large networks, and propose a design. We conclude that LaSCO has characteristics that enable its use on different types of systems throughout the process of precisely expressing a policy, understanding the implications of a policy, and implementing it on a system.