On the microlevel, cusps are formed during delamination crack growth under mode II loading conditions. In this work, two different approaches to simulate this process are presented. Firstly a cohesive zone method where cohesive segments are introduced between a pair of neighbouring elements when the traction between those elements exceeds the strength. And secondly the thick level set method, which allows for a staggered solution scheme. Both methods successfully predict the inclined cracks that form initially if constitutive laws are chosen carefully, but both have difficulties to simulate final failure.