The vibratory response of a long slender riser, made of composite materials and subject to an ocean current, is examined for a range of conditions. A major focus of this study is the performance of composite materials when used for risers. The influence of the number of modes of vibration is studied, as is the influence of the mass ratio and the value of the damping coefficient. The flow past the riser is represented by a shear flow, ranging from at the lower end of the riser to at the upper end of the riser. The riser vibration is treated as a coupled fluid-flow/vibration problem. The fluid-flow equations are represented by a large eddy simulation model for the wake turbulence present in the flow. Strip theory is used to represent different forcing locations along the length of the riser. Since the composite riser has a material damping that is frequency dependent (it decreases with increasing frequency), its response is different from, say, a steel riser with a constant material damping. The composite riser, with variable damping, has a larger rms displacement than a riser with constant damping, primarily because of the smaller mass ratio. The vibration amplitude is found to increase with an increase in the number of modes.