Twenty-three tests have been used to evaluate a simplified design analysis for the ultimate resistance of fibre-reinforced polymeric box beams. This analysis assumes failure in any one of five distinct modes and is based on linear elastic thin-wall theory. Four different hollow box profiles have been tested in three-point bending. They were manufactured by the pultrusion process. The material is a vinylester-based matrix, reinforced with two types of continuous E-glass fibre. For the assessment, it has been necessary to measure the section flexural moduli and material compressive strengths. These vary according to the composition by weight of the two fibre reinforcement types. The strengths of the box beams and their modes of failure are reported. When the beam span is long, the design analysis can predict ultimate resistance accurately, providing that a modification is made for thick walls. However, at short spans the analysis is inappropriate because the mode of failure is not in one of the modes assumed in the design analysis.