This paper presents a direct method for determining natural frequencies of lateral modes of vibration for marine risers in deep water This method applies to marine risers that are vertical, relatively straight, and attached at both ends. The method is particularly useful for determining natural frequencies of higher modes that are sometimes difficult to obtain analytically or numerically. Comparisons of numerical results with published data show that even though the method of solution is approximate, the calculation procedure gives useful engineering results. The algorithm is based on classical vibration theory and can easily be programmed on portable computers for direct use on offshore oil rigs.