The growth of the aeronautical sector leads to the growth of polymer composites application, creating new demand for components applications in complex dimensions and shapes. Regarding different methods of draping 2D fabric into a 3D format, the concern is to keep the fabric properties and characteristics, since fiber orientation is modified after draping. For that purpose, this study aims to evaluate the drapability capacity of 2D dry fibrous fabrics (plain, twill, satin, non-crimp-fabric 0/90, and ±45) into a complex geometry, i.e., spherical indent. The energy required to drape fabric is composed of fabric deformation mechanisms (shear and bending), which were used together with microscopic deformation analysis to determine the appropriate fabric architectures with the highest malleability. Both NCF fabrics presented high energy and roughness on the fabric surface due to the folding effect of stitching. On the other hand, plain and twill weave fabrics required lower energy to drape but demonstrated higher fiber misalignment and deformation. The satin warp/weft relation favored shear and bending mechanisms, presenting better uniformity in load distribution, symmetry on drape capability, lower deformation degree, and lower fiber misalignment. Despite the intermediate load and energy required for drape, ANOVA and optimization methods confirmed that satin fabric showed better malleability behavior for complex geometries applications.