On the microlevel, cusps are formed during delamination crack growth under mode II loading conditions. In this work, the Thick Level Set (TLS) approach is used to simulate the cusp formation process. A plasticity model for polymers is implemented in the TLS method and a new loading scheme is devised to deal with permanent strain. A numerical test case is analysed under shear loading to mimic the fracture process which has been observed in mode II delamination growth in fiber reinforced polymer. By varying the cross-section geometry, different load-displacement behaviours and fracture morphologies are produced. The cross-section geometries considered includes variation in size and shape of longitudinal sides (grooves). The approach presented predicts the cusp formation, which begins with the initiation of a series of inclined cracks distributed along the length of the specimen, and can reach final failure.