The tensile failure of fiber-reinforced composites in 2D (l-ply) and thin multi-ply samples has been studied numerically in order to assess the role of dimensionality on the absolute magnitude, reliability, and size scaling of composite strength. Single-ply tapes, often used in model calculations because of the simplifications attending the reduced dimensionality, and 2-ply tapes are shown to have (i) lower strengths than 4-ply specimens, with the latter approaching 'bulk' response, and (ii) broader failure probability distributions than 4-ply samples. These two effects together indicate that using a 1-ply or 2-ply geometry to investigate composite strength size effects and reliability, or to compare against real composites, is not quantitatively accurate. Calculations are also performed on the same systems but with fiber 'pull-out' loads, i.e. the residual load carrying capability of broken fibers in the composite, essentially eliminated. Such a model approximates the 'chain of bundles' models widely developed for prediction of composite failure. In the absence of fiber pull-out, the composite strength is much lower and again more broadly distributed. Overall, the present results suggest that simplified analytic and computational models based on a 2D tape geometry and/or neglecting fiber 'pull-out' must be viewed with caution in applications to real composite systems. (C) 2000 Elsevier Science Ltd. All rights reserved.