Hydrographic observations in an area immediately northeast of Taiwan in April 1989 indicate an on-shelf intrusion of Kuroshio water across a sharply curved continental shelf break. It appears that a part of the Kuroshio on the cyclonic side overran the shelf break and penetrated northward as a shallow surface current. The remainder of the Kuroshio, presumably affected by the shoaling topography, largely turned and ran along the shelf break to the northeast. Between the two, the flow was weak and disorganized. Conservation of potential vorticity and constancy of the Bernoulli function in an analytical, reduced-gravity model of the incidence of a baroclinic current upon a step shelf lead to an on-shelf flow field that is compatible to the observed hydrographic distributions. In particular, the integrated balance of along-step momentum yields an expression of the angle of intrusion in terms of the incidence angle and of the ratio of step depth to the depth of the upper layer of the ocean. In addition, the transport of the intrusion is shown to be equal to the product of the depth ratio squared and the incident transport. Calculations for the condition of the April survey yield results in agreement with the observation. ¿ American Geophysical Union 1992