We present a new analytical model for a horizontal axis cyclorotor-based wave energy converter (WEC). A number of cyclorotor-based WEC concepts and models, with different numbers of hydrofoils, have previously been studied. Our model is derived for a horizontal cyclorotor with 2 hydrofoils. The governing equations are optimised and converted to the polar coordinate system. The mechanical model is based on Newton's second law for rotation. Rotation is considered in two-dimensional potential flow, for both monochromatic and panchromatic waves, including waves generated by the rotating rotor, and viscous losses. The developed model is very convenient for modelling, analysis and control design for a cyclorotor based WEC. The authors of this work have derived new, exact, analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time, compared to previous models, and increase the accuracy of the results. We present the results of free rotation simulations for the rotor in monochromatic and panchromatic waves obtained with the use of the newly derived equations.