A number of studies have been reported recently where the dynamic response of a TLP is obtained in the time domain, through step by step integration of the equations of motion, using Morison’s equation to predict the hydrodynamic forces on the members. One difficulty with this approach, as reported by a number of authors, is the computation of the heave hydrodynamic forces acting at the base of the main vertical cylinders as well as the fluid reactions to the heave motion of these members. To help in the selection of these forces a number of parametric studies have been conducted on a single vertical truncated cylinder using linear potential theory. Periods from 4 to 18 seconds (wave period or period of cylinder oscillation corresponding to diffraction or radiation, respectively) and cylinder aspect ratios (D/h, diameter/draft) varying from 0.05 to 1.6 were used in the analyses with water depths exceeding 3000 ft. The results have been arranged in dimensionless form and are shown in graphs. Simplified formulae have then been fitted to these results in order to obtain approximate expressions which can be used in practice. Although the heave forces and radiation coefficients were of primary interest to make the study complete the horizontal forces and rocking moments (surge and pitch diffraction forces) and the corresponding radiation coefficients were also computed, plotted, and fit with approximate formulae.