The several manufacturing stages a braided textile must go through until its completion, append random material defects in terms of geometry. These uncertainties are not only difficult to predict, but also hard to be minimized, and since they mostly occur in lower scales, they significantly affect the response of materials with such a heterogeneous nature. Realistic numerical, multiscale models should account for the variability of their representative volume elements, thus have the ability to include spatial randomness. In this work, novel modeling strategies are proposed for the consideration of geometrical uncertainties of 3D braided composites. The problem of distorted yarns due to high levels of compaction is simulated with a technique inspired from random inclusion studies, able to describe the yarn section of the mesoscale with a 1D random field. This approach can randomize sections of any shape. The problem of yarn waviness (stochastic deviations from the hypothetical perfect yarn trajectory) is dealt with a formulation based on Gaussian process modeling (a.k.a. Kriging), where 1D Gaussian random fields are appropriately tailored to match the systematic yarn path (trend). Statistical characteristics (e.g. correlation, variance etc.) gathered from physical samples can be included in the proposed approach in a straightforward manner, while several other advantages over older techniques are discussed. All modeling techniques discussed herein, are suitable for finite element simulations. Applications for a 3D braided multiscale model (based on previous work1 by the authors) are presented, emphasizing on the variability of the elastic tensor of the macroscale due to each type of uncertainty. The voxel method is used for the discretization of the imperfect volume element. The need for realistic uncertainty quantification is highlighted, while the coupling of manufacturing processes and structural mechanics is more crucial than ever.