Forces and motions imposed upon a moored buoy system by the oceanic environment are investigated using numerical methods on a digital computer. Equations of motion for axisymmetric buoys are developed for six degrees of freedom including cross-coupled hydrostatic and hydrodynamic forces. Equations of motion for the mooring cable are developed to allow simultaneous axial and transverse wave propagation. A unique method of characteristics numerical technique is shown for digital computer simulation of cable dynamics. The equations of motion for the buoy and its mooring cable are coupled and are excited by winds, currents, and a quasi-random wind wave model. Simulated buoy system parameter response characteristics are compared with response characteristics observed from actual oceanographic buoy system moorings.