If a vertical axis wind turbine is mounted offshore on a semi-submersible, the pitch motion of the platform will dominate the static pitch and dynamic motion of the platform and wind turbine such that the effect of tower tilting on the aerodynamics of the vertical axis wind turbine should be investigated to more accurately predict the aerodynamic loads. This paper proposes certain modifications to the double multiple-streamtube (DMS) model to include the component of wind speed parallel to the rotating shaft. The model is validated against experimental data collected on an H-Darrieus wind turbine in skewed flow conditions. Three different dynamic stall models are also integrated into the DMS model: Gormont's model with the adaptation of Strickland, Gormont's model with the modification of Berg and the Beddoes–Leishman dynamic stall model. Both the small Sandia 17 m wind turbine and the large DeepWind 5 MW are modelled. According to the experimental data, the DMS model with the inclusion of the dynamic stall model is also well validated. On the basis of the assumption that the velocity component parallel to the rotor shaft is small in the downstream part of the rotor, the effect of tower tilting is quantified with respect to power, rotor torque, thrust force and the normal force and tangential force coefficients on the blades. Additionally, applications of Glauert momentum theory and pure axial momentum theory are compared to evaluate the effect of the velocity component parallel to the rotor shaft on the accuracy of the model. Copyright © 2013 John Wiley & Sons, Ltd.