For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected linear short-crested wave riding on a uniform current is given. The analysis is based on the conventional shallow water Airy wave theory and the direction of the main wind direction can make any direction with the current. A consistent derivation of the wave spectrum taking into account current and finite water depth is used. The numerical results show a significant effect of the water depth, the directional spreading and the current on the conditional mean wave profile. Extensions to higher order waves are finally discussed.

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