Our modelling of thermal damage in carbon fibre composites after lightning strike aims to simulate coupled electric current flow and thermal fields in composites structures during lightning strike, and associated degradation of the material. (The lightning strike protection is an essential part of any modern development, such as aircraft wings or wind turbines' rotating blades.) Our main objective is to develop a qualitative mathematical model and an effective computational method to predict the composites behaviour during lightning strike through a robust understanding of the physics of the associated high-voltage and high-current processes.