The increasing complexity of transport vehicles means that more powerful finite element models are needed to simulate their crash behaviour. As existing models' calculation times are long and cannot effectively optimize structures in terms of peak moment and energy management, they should only be used as a final verifying tool. Distinct analytical models have been developed to determine the resistance to collapse of thin-walled structures subjected to a bending load. Part I of this paper concerns the theoretical prediction of bending strength in the pre-failure range for thin-walled structures of relatively complex geometry. Two types of buckling are considered: elastic and plastic.