The power absorption capability of a floating oscillating body depends on the proper wave-structure interaction. A wave energy converter (WEC) device would capture the wave power as the system radiates waves in the opposite direction (phase) to the incoming waves. Hence, in order to evaluate the initial performance of a point absorber wave energy converter, determination of radiation force is crucial to design and optimal control of wave energy absorption. In this paper, once the hydrodynamic parameters are obtained for a heaving vertical-cylinder buoy, the equation of motion for the system has been considered upon the Cummins integro-differential equation. Numerical analysis of this type of equation could be computationally demanding due to the presence of a convolution term. Therefore, a program was written using the high-level language in MATLAB and the expression for the radiation force in the equation of motion has been substituted with a linear state-space model. The results of the frequency domain analysis in the range of 1-2 radians per second are implemented into the model which corresponds to the predominant wave conditions of the offshore region in Persian Gulf. The proposed open source model compared to direct calculation of the convolution integral in the equation of the motion provides highly accurate prediction and maintains system stability. The model would also be computationally cost effective for higher degrees of freedom since other codes are practically not available.