Fiber-reinforced plastic (FRP) beams are thin-walled or moderately thick-walled open or closed sections consisting of assemblies of flat panels. We present a computational approach with the computer program FRPBEAM (1994) for the response evaluation of pultruded FRP beams in bending. This program combines micro/macro-mechanics analyses with the Mechanics of Laminated composite Beams (MLB) model and an explicit stability solution to analyze, design, and optimize FRP shapes. In FRPBEAM, the ply stiffnesses are predicted by micromechanics formulas, based on the fiber volume fraction of each lamina, and the panel laminate properties are computed from the ply stiffnesses and macromechanics. The MLB model is used to analyze the overall response of FRP beams in bending, and the Tsai–Hill failure criterion is adopted to predict first-ply-failure loads. An example of a laminated box beam is used to demonstrate the accuracy of the computer program for predicting beam displacements and ply stresses in relation to finite element analyses. A stability Rayleigh–Ritz method is included in the program and used to evaluate the critical buckling loads for pultruded I-beams. Through parametric studies with FRPBEAM and a multiobjective optimization scheme, the fiber architecture of an existing I-beam is optimized, and based on a recommended practical design, the I-beam section is produced by pultrusion and subsequently tested in bending. The predicted response with FRPBEAM correlates well with the experimental results. As illustrated by design analysis and optimization examples presented in this study, the experimentally and numerically verified computer program can be used to analyze existing FRP shapes and develop new optimized shapes for the civil structural market.