When a continuum approach is considered for textile reinforcements, the internal loads are described by a stress tensor. The mechanical behaviour of the textile material is very much dependent on the fiber directions, and the frames defined from warp and weft directions are preferred to write the stress components. The exterior loads in these frames permit to define tensile and pure shear states. Nevertheless, these frames are generally not orthogonal. The relationships between the exterior loads and the different stress components are analyzed in the present paper, and, in particular, the relationship between direct stress components and longitudinal loads on one hand, and shear stress components and transversal loads on the other hand. When dealing with textile materials, the exterior loads in the direction of the fibres and transverse to the fibres define the pure tensile and pure shear state. It is shown that the covariant stress component matrix is diagonal in a pure tensile loading and that the first mixed direct stress components are equal to zero in a pure shear loading. In these cases, the direct relationship between the stresses and the loadings are given. This is applied to the cases of the picture frame test, the biaxial tensile test or of a combined tension-shear test.