This paper focuses on the numerical energy absorption behaviour of pultruded circular and square cross sectional glass-polyester composite tubes under an axial impact loading case. In order to capture the typical failure modes such as delaminations, lamina bending, axial cracks and fibre fracturing, a new innovative approach was used using multiple shell elements, cohesive elements and pre-defined seams. To predict the correct peak crush load and the corresponding energy absorption, the importance of the numerical modelling of multiple delaminations and triggering are discussed. Two types of triggering were chosen for the study. Finally, the results of this numerical investigation are compared with experimental data. The commercially available finite element code ABAQUS V6.7-3 Explicit was used for this study.