Using plasticity limit theorems, transverse strengths for unidirectionally reinforced composites containing fibers with hexagonal cross sections are found and compared with earlier “exact” values found by Drucker for symmetric deformation. Using unsymmetric deformation modes, upper bounds are found which are lower than the values found by Drucker for volume fractions of fibers between 0.40 and 0.58. By extending the symmetric analysis, it has been found that for nonuniform hexagonal fiber sizes, the transverse limit strength is higher (for the same volume fraction) than for the uniform size case. Also, selected agglomerations can greatly increase transverse limit strengths.