The (first-order) wave forces on structures interacting with ocean waves may be represented by complex transfer functions in the frequency domain or by convolution integrals in the time domain. The integration kernels are causal for radiation forces, but not necessarily so for excitation (scattering) forces. As a convenient approximation, these integrals may be replaced by a finite-order system of differential equations with constant coefficients. This method is applied to a heaving cylinder with a vertical axis, and good approximations are obtained when the order of the differential equation system is three for the radiation force and five for the excitation force. The corresponding state-space model for the heave motion response due to the incident wave elevation has an order of 10, but it is demonstrated that it is possible to reduce the order to five without increasing the inaccuracy in the heave motion too much.