This paper presents analytical and finite element (FE) studies on behavior of FRP (fiber reinforced polymer) composite strengthened reinforced concrete (RC) beams under torsional loading. Presence of torsion significantly changes the failure mode of RC members and therefore it is essential to understand the efficiency of FRP strengthening under torsion. This study tries to fill the knowledge gap existing in this important area of research by carrying out analytical and FE studies. An improved softened membrane model for torsion (SMMT-FRP) considering the influence of FRP composites on the compressive behavior of cracked concrete is proposed. A new tension stiffening relationship of concrete is also recommended for improved analytical predictions. The analytical study is accompanied by a full scale nonlinear FE study using commercial package ABAQUS. Parameters such as post cracking stiffness, peak torque and peak twist are accurately captured by the improved SMMT-FRP. Finite element predictions are also compared with analytical predictions and experimental results. Comparisons indicate a reasonably good agreement of both analytical and FE results with test data. FRP strengthening increased the post-cracking stiffness, ultimate strength and localized the damage. © 2016 Elsevier Ltd