The understanding of the non-Schmid behavior in shape memory alloy NiTi is considered a significant breakthrough because this alloy still remains enigmatic. We utilize an Eshelby-Stroh formalism in conjunction with Molecular Statics-Peierls stress calculation to predict the experimental CRSS results for three different crystal orientations and tension-compression cases. These combination of tools incorporating elastic anisotropy and core displacements are necessary to develop a precise understanding of non-Schmid behavior. We note the different extents of core spreading produce a highly asymmetric tension-compression behavior and strong orientation dependence governed by the non-glide shear and normal stress components. The experimental results and empiricism free modeling produces excellent agreement, and most importantly enlisting scientific insight into the shape memory response.