Fracture properties of isotactic polybutene-1 have been investigated. Fracture tests have been conducted and relevant properties at initiation have been determined according to linear elastic fracture mechanics. Two distinct fracture mechanisms have been identified, one of them causing partial instability during crack propagation. Numerical modelling has been performed using a cohesive zone approach. In particular, the identification of suitable cohesive laws has been tried using parametric identification and two different experimental methods. Results suggest that two different cohesive laws may be needed in order to describe crack initiation and crack propagation.