Fracture in crystal lattices usually occurs with discrete atomic bond breakages around the crack tip. WS2 involves three-layer atomic structures, where the atomic stress near the crack front exhibits thickness dependence and significantly relies on the local distortion of lattice geometry. We show that the T-stress obtained by over-deterministic methods, and the continuum circumferential stress, are limited in predicting the nanocrack kinking of WS2 strips by molecular dynamics simulations. As the far-field displacement loads, the T-stress initially increases in negative, followed by a slight jump at the initiation of kinking, and the continuum circumferential stress cannot accurately capture the variation of atomic stresses at the crack tip. This can be attributed to the local anisotropy in atomic lattices, and the crack preferentially extends in the zigzag direction of the local maximum energy release rate. Our work might provide insights into the fabrication and assembly of WS2 nanodevices.