Fibre reinforced polymers (FRPs) have demonstrated good performance in retrofitting deteriorated reinforced concrete structures. However, there remains a paucity of information on the performance of available FRP strengthening systems at elevated temperatures, and the perceived susceptibility of these systems to fire continues to discourage their use in some applications. To begin to address this issue for the specific case of strengthening rectangular concrete columns with FRP wraps, an experimental and analytical study has been performed. An objective of the study is to develop validated computational models that can be used to perform parametric analyses and suggest design guidelines for these types of structural members. This paper presents the development and partial verification of a computational model that can simulate the structural behaviour of a short or slender, concentrically or eccentrically loaded, unwrapped or FRP wrapped column under both ambient and fire conditions. Results of initial analytical studies, including validation of the model using test data available in the literature, are presented.