Dynamic programming and invariant imbedding concepts are used to transform the two-point boundary-value problem of the theory of thin beams into initial-value problems that can be solved effectively by analog or digital computers. To demonstrate the computational feasibility of the methods, an example of a uniform beam of unit length, free at the left end and cantilevered at the right, was chosen, and the deflection was computed by three methods: a reference solution was computed by a segmenting technique, and the deflections were then computed by dynamic programming and by invariant imbedding. Results indicate excellent agreement among the various solutions. 26 pp. Ref.