A new failure criterion for fiber tows (i.e. yarns) is developed based on a micromechanical model using mechanics of structure genome (MSG) and deep learning neural network. The proposed failure criterion can be applied to yarns in mesoscale textile composites modeling while capturing the failure initiation at the fiber and matrix level. A plain weave fiber reinforced composite material example is used to compute the initial failure strength constants based on the proposed yarn failure criterion. To study the accuracy and efficiency of the failure criterion, a comparison to a meso-micro coupled model explicitly capturing the failure initiation at fiber and matrix level is performed. Moreover, the differences between the mesoscale modeling results based on the proposed criterion and other yarn failure criteria (i.e. maximum stress, Tsai-Wu, and Hashin) are studied. Lastly, the failure envelope analysis is carried out using MSG solid model to further demonstrate the accuracy and efficiency of the new yarn failure criterion under combined loading conditions.