A three-dimensional numerical model for shallow-water flow with the assumption of hydrostatic pressure has been applied to oscillatory laminar flow around a conical island of small side slope (8°). The model is (mainly) second-order accurate in space and time with advection in conservation form. This form of model is effectively a boundary-layer solution with imposed depth-integrated continuity. To reproduce experimental conditions particular care was required for boundary conditions to account for seiching in the flume. The model predicted the wide range of wake structures observed experimentally and described in Part 1 (Lloyd, Stansby & Chen 2001), from symmetric with weak vortex pairing to complex vortex shedding.