Typically, most of the brittle composite tubes exhibit circumferential delamination, lamina bending, axial cracking and brittle fracturing when subjected to static and dynamic loading conditions. In this work, a new innovative approach was adopted to model the above said failure modes using cohesive elements under an axial impact loading case. The circular and square cross sectional pultruded profiles made of glass-polyester were considered for the study. A numerical parametric study has been conducted to study the effect of the delamination on the failure patterns and the corresponding energy absorption using a single layer and two layers of shell elements. To predict the peak crushing load and the energy absorption, the importance of the adequate numerical modelling of triggering is discussed. All numerical simulations were carried out using the commercially available finite element code ABAQUS V6.7-3 Explicit. Finally, the results of this comprehensive numerical investigation are compared with previously published experimental results [1]. Part II of this paper deals with the influence of multiple delaminations and modelling of axial cracks on the deformation patterns and the effect of initial geometric imperfections on the energy absorption.