Monte Carlo simulation and theoretical modeling are used to study the statistical failure modes in unidirectional composites consisting of elastic fibers in an elastic matrix. Both linear and hexagonal fiber arrays are considered, forming 2D and 3D composites, respectively. Failure is idealized using the chain-of-bundles model in terms of δ-bundles of length δ, which is the length-scale of fiber load transfer. Within each δ-bundle, fiber load redistribution is determined by local load-sharing models that approximate the in-plane fiber load redistribution from planar break clusters, as predicted from 2D and 3D shear-lag models. As a result the δ-bundle failure models are 1D and 2D, respectively. Fiber elements have random strengths following either a Weibull or a power-law distribution with shape and scale parameters ρ and σδ, respectively. Under Weibull fiber strength, failure simulations for 2D δ-bundles, reveal two regimes: When fiber strength variability is low (roughly ρ > 2) the dominant failure mode is by growing clusters of fiber breaks, one of which becomes catastrophic. When this variability is high (roughly 0 < ρ < 2) cluster formation is suppressed by a dispersed failure mode due to the blocking effects of a few strong fibers. For 1D δ-bundles or for 2D δ-bundles under power-law fiber strength, the transitional value of ρ drops to 1 or lower, and overall, it may slowly decrease with increasing bundle size. For the two regimes, closed-form approximations to the distribution of δ-bundle strength are developed under the local load-sharing model and an equal load-sharing model of Daniels, respectively. The results compare favorably with simulations on δ-bundles with up to 1500 fibers.