The paper studies the prediction of the crack growth of the brittle and ductile fracture of the structural materials. Crack extension is simulated by means of element extinction algorithms. The principal effort is concentrated on the application of the cohesive zone model with the exponential traction separation law and on the cohesive zone modelling. Determination of micro‐mechanical parameters is based on the combination of static tests, microscopic observation and numerical calibration procedures. The attention is paid on the influence of initial value of J‐integral and the slope of R curve which is modelled by 3D FEM. The aim of this paper can be seen in verification of the application of the cohesive model based on the separation law, experimental and calibration procedure inevitable for the determination of the cohesive parameters for the modelling.