We present a one-dimensional model of the mass-loading of the solar wind by cometary ions which predicts a singularity in the mass-loaded flow at M=2. Further, a subshock occurs when the flow speed reaches M≈1.15. The shape of the cometary bow shock in two dimensions is predicted, by requiring that the flow Mach number of the shock is 2 taking the velocity component normal to the shock surface. The Mach number results compared favourably with observations at comet Halley. ¿American Geophysical Union 1991