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Abstract: The airn of this work is to darify the validity of ship wave ray theories at and near the ship's surface. As previous numerical investigations have led to ambiguities due to a breakdown of the ray analysis near the bow and stern stagnation points, we shall take care far the surface tension effect in order to milden such deficiencies; then the wave length never surpasses a positive minimum length which is attained at the boundary of a finite waveless zone around a stagnation point. It is found, however, that the ray equations degenerate at these boundaries, and that rays can be traced into the far field only if their starting point is selected outside a finite belt surrounding the waveless zone. For a dass of bi-circular prismatic struts of infinite downward extent, we investigated two alternative formulations of the free surface condition and their implications for the ray geometry. For low speeds we found in both cases an increase of the Kelvin wave cusp angle due to capillarity. We extended the ray tracing to capillary waves ahead of a blunt bow.