Tidal energy is an attractive renewable resource given its predictability. The production of reliable, efficient and cost-effective tidal energy turbines requires the development of computer models for assessment and design optimisation of turbine performance. Blade element momentum theory (BEMT) models are attractive to turbine designers as they have a very low computational cost compared to CFD models. In this paper, we develop a BEMT model for high solidity and highly loaded vertical axis tidal turbine rotors which traditional BEMT models are incapable of modelling. The double multiple stream-tube model employs a graphical approach for determination of axial induction factors rather than the iterative approach used in traditional BEMT models. Corrective methods to account for dynamic stall, flow expansion, and finite aspect ratios are also implemented in the model. Model performance is assessed against experimentally measured power performance data of both low and high solidity rotors. The model reproduced peak efficiency values to within 2.5% for a low solidity wind turbine, 8% for a high solidity wind turbine and to within 10% for a high solidity tidal turbine in confined flow.