Textile composites offer challenges for modeling their mechanical behavior due to the complex structure of the heterogeneity. This work examined issues in modeling textile composites at the scale of the fiber bundle (mesoscale). It has been observed that due to geometric effects of nesting, prismatic unit cell models are not able to contain realistic fiber volume fractions. Simplifying assumptions were proposed to overcome this problem. Example composites composed of plain weave and triaxial braid reinforcement were modeled using the finite element method. Some details of the models are described. Good results were obtained when predicting elastic material constants. A failure criterion based on multicontinuum theory (MCT) was devised to predict initial failure of the matrix within the tows of the triaxial braid. It was found that if the mesoscale model was used in conjunction with experimental data to determine the criterion coefficients that the failure predictions appear insensitive to details of the mesoscale model.