The present paper describes the numerical simulation of random wave forces acting on a section of fixed slender vertical cylinder near the free surface, taking account of the intermittency of submergence. Time histories of water particle kinematics corresponding to a specified wave spectrum are generated using linear numerical transforms and corresponding force time histories at different sections are computed using the Morison equation. Analytical predictions of various statistical properties of water particle kinematics and forces for the intermittent flow are compared with results of the numerical simulations. These include the probability density of particle kinematics, the spectral density of the force, the probability density of force maxima, and the mean and standard deviation of the force maxima. In general, the agreement is found to be quite satisfactory. The effects of simulation time and random phases on the mean and standard deviation of intermittent force maxima are also investigated.