A theoretical model of acoustic propagation in the ocean around a conical seamount is presented. The sea surface and the surface of the seamount are assumed to be perfect reflectors, with the apex of the seamount just touching the surface of the ocean. This geometry is such that the boundary surfaces of the channel can be represented by the surfaces of a separable (spherical polar, origin at the apex) coordinate system. The solution of the Helmholtz equation for a point source in the channel is shown to consist of a sum of normal modes in which the variable is angular depth, and in which the mode amplitude functions contain the entire range/azimuth dependence of the field. These mode amplitude functions show that, in each mode, there is a sharply defined shadow zone lying behind the seamount, and surrounding the shadow is an ensonified region where the field shows very rapid spatial oscillations. This oscillatory behavior indicates that strong interference occurs within a single mode. An important feature of the model is that it specifies completely the three‐dimensional field around the seamount, giving both amplitude and phase. The theory is therefore relevant to studies of the performance of acoustic arrays in this type of environment.