Closed-form mathematical expressions are derived for the fatigue damage of structures due to ocean waves. The expressions incorporate relationships between wave height and stress range, between stress range and number of cycles to failure (1. e. a fatigue curve), and the probability distribution for the occurrence of wave heights. The expressions can be utilized to predict the fatigue damage resulting from a single sea state, from a storm, or during the service life of a structure. In addition, the fatigue life of a structural element can be determined directly from the stress range resulting from the design wave, or conversely, an "allowable stress range" can be determined for the design wave which will insure a specified fatigue life. Example applications are given for areas having wave climates similar to the North Sea and similar to the Gulf of Mexico. INTRODUCTION: Ocean waves encountering a structure cause the stress in each structural element to cycle. The accumulated effect of the stress cycles can cause elements of an improperly designed structure to fail by fatigue. In general, from the standpoint of fatigue damage there are two categories of structures:structures with a response to ocean waves which is significantly affected by dynamic amplification andstructures without significant dynamic amplification. This paper will be restricted to the last category of structures for which dynamic amplification can be neglected for fatigue analyses. The current state-of-practice for the fatigue analysis of ocean structures is summarized by Marshall in Reference 1. The analysis of the fatigue life of a structure requires a lengthy numerical calculation procedure which utilizes:The appropriate S-N curve for the structural element being considered. The S-N curve relates the number of cycles to failure, N, for a cyclic stress range, S, having a constant amplitude (see Figure 1).The Palmgren-Miner rule which predicts the cumulative effect of stress cycles having different amplitudes.An empirical relationship between the wave height encountering the structure and the stress range induced in the structural element, for all wave heights that the structure will encounter.A statistical description of the occurrence rates for wave heights which the structure will encounter during its life. The numerical analysis consists of breaking the range of wave heights into discrete bands and determining the number of waves which will occur in each height band. For each height band, the stress range corresponding to the mid-band height is determined for the structural element. Then the S-N curve is used to determine the fatigue damage for the element due to the stress range associated with each height band. The final step is to accumulate the damage for all height bands using the Palmgren- Miner rule. This procedure can be undertaken manually in a straightforward, but time- consuming, manner or can be programmed for a digital computer.