A limiting property governing the thermomechanical behavior of composites is the strength transverse to the fibers. The present study investigates the dependence of this property on the distribution of fibers in the cross-section of a unidirectional composite. The approach taken is to consider actual distributions, which are arbitrary and are not necessarily described by random or periodic distributions. A fundamental issue in studying non-uniform distributions is the size of a representative volume element (RVE). By the use of an actual radial distribution function obtained for a ceramic-matrix composite by quantitative stereology in conjunction with a simulation technique developed in this study, the RVE size is investigated with respect to initiation of debonding and radial matrix cracking - two basic mechanisms governing the transverse strength of composites. Tensile loading transverse to the fibers and residual stresses induced by thermal cooldown are considered separately as loading modes for transverse failure. The results provide some useful insight into the importance of non-uniformity of fiber spatial distribution with regard to the transverse failure of composites. A limiting property governing the thermomechanical behavior of composites is the strength transverse to the fibers. The present study investigates the dependence of this property on the distribution of fibers in the cross-section of a unidirectional composite. The approach taken is to consider actual distributions, which are arbitrary and are not necessarily described by random or periodic distributions. A fundamental issue in studying non-uniform distributions is the size of a representative volume element (RVE). By the use of an actual radial distribution function obtained for a ceramic-matrix composite by quantitative stereology in conjunction with a simulation technique developed in this study, the RVE size is investigated with respect to initiation of debonding and radial matrix cracking - two basic mechanisms governing the transverse strength of composites. Tensile loading transverse to the fibers and residual stresses induced by thermal cooldown are considered separately as loading modes for transverse failure. The results provide some useful insight into the importance of non-uniformity of fiber spatial distribution with regard to the transverse failure composites.