This paper presents experimental results of the effect of random waves on the flow drift viscous damping forces acting on a vertical circular cylinder. The experiment was carried out using a forced oscillation apparatus, so a wide range of parameter combinations was easy to obtain. The effect of velocity ratio, reduced velocity and period ratio were investigated. Results from the experiment have revealed some different features between the effect of random waves and that of regular waves on the slow drift viscous damping forces. This problem was also studies using a numerical method in which the hydrodynamic forces were obtained from simulating the flow field using a finite difference method. Results of slow drift viscous damping force coefficients show generally good agreement between computed and measured values.