Presence of torsional loadings can significantly affect the flow of internal forces and deformation capacity of reinforced concrete (RC) columns. It increases the possibility of brittle shear failure leading to catastrophic collapse of structural members. This necessitates accurate prediction of the torsional behaviour of RC members for their safe design. However, a review of previously published studies indicates that the torsional behaviour of RC members has not been studied in as much depth as the behaviour under flexure and shear in spite of its frequent occurrence in bridge columns. Very few analytical models are available to predict the response of RC members under torsional loads. Softened truss model (STM) developed in the University of Houston is one of them, which is widely used for this purpose. The present study shows that STM prediction is not sufficiently accurate particularly in the post cracking region when compared to test results. An improved analytical model for RC square columns subjected to torsion with and without axial compression is developed. Since concrete is weak in tension, its contribution to torsional capacity of RC members was neglected in the original STM. The present investigation revealed that, disregard to tensile strength of concrete is the main reason behind the discrepancies in the STM predictions. The existing STM is extended in this paper to include the effect of tension stiffening for better prediction of behaviour of square RC columns under torsion. Three different tension stiffening models comprising a linear, a quadratic and an exponential relationship have been considered in this study. The predictions of these models are validated through comparison with test data on local and global behaviour. It was observed that tension stiffening has significant influence on torsional behaviour of square RC members. The exponential and parabolic tension stiffening models were found to yield the most accurate predictions. Copyright © 2015 Techno-Press, Ltd.