The principal stress rotation is one of the most important features of the stress state in a seabed subjected to wave loading. Most prior investigations focused their attention on the cyclic behaviour of soil deposits under the circular rotation stress path based on the analytical solutions for a seabed of infinite thickness. In this paper, the nonstandard elliptical, i.e., non-circular, rotation stress path is shown to be a more common state in the soil sediments of a finite seabed with an alternating changeover in stress due to a travelling regular wave. Then an experimental investigation in a hollow cylinder triaxial-torsional apparatus is conducted into the effect of the nonstandard elliptical stress path on the cyclic strength. A special attention is placed on the difference between the circular rotation stress path and the elliptical rotation stress path. The results and observations show that the shear characteristics for the circular rotation stress path in the literature are not applicable for analyzing the cyclic strength of sand in a finite seabed, and also indicate that due to the influence of three parameters about the size and the shape of a nonstandard ellipse, the cyclic strength under a nonstandard elliptical rotation stress path is evidently more complex and diversified as compared with that under a circular rotation stress path. Especially the influence of the initial phase difference on the cyclic strength is significant.