Supersonic plasma flow around an object large compared with the Debye distance is treated using an isothermal gas dynamics model. The case of (initially) subsonic flow has been studied previously using this model, the motivation then being the use of Langmuir probes. In supersonic plasma flow Mach cones describing weak discontinuities rather than shock waves are predicted. A comparison has been made with particle-in-cell simulations carried out by Willis et al. (Willis, C. T. N., Allen, J. E., Coppins, M. and Bacharis, M. 2011 Phys. Rev. E, 84, 046410), where such Mach cones are observed. Other features cannot be explained by the isothermal gas dynamics model, these include the appearance, at high supersonic velocities, of an ion-free region downstream.