In this chapter, we formulate an approach to computation with beam theory that culminates in a code that solves the problem of a beam with any boundary conditions and any form of distributed loading. The approach uses the tools of numerical integration to accomplish the primary tasks associated with solving the differential equation. We extend the code to incorporate point loads and end by implementing a code that solves the multispan beam problem. The main goal of the chapter is to illuminate the theory by organizing the solution process for beams into a tidy algorithm. A primary benefit of the developments of this chapter is a computational framework that can quickly solve a broad array of problems with different loading and support conditions, enabling systematic exploration of the behavior of beams.