An axisymmetric numerical model has been developed to simulate Ward's (1972) laboratory experiments. It was shown by Davies-Jones (1976) that this experiment is more geophysically relevant than all previous experiments in that Ward's experiment exhibits both dynamical and geometrical similarity to actual tornadoes. Major results are 1) the core size versus inflow angle relationship agrees very nearly with Ward's measurements, 2) the numerical and laboratory surface pressure patterns are in agreement, and 3) it is demonstrated that the core radius is independent of the Reynolds number at high Reynolds number (Ward's data also exhibit this behavior). Based on this axisymmetric model some speculation concerning the nature of the asymmetric multiple vortex phenomenon is made. Furthermore, the numerical model allows the examination of the interior flow field. As a consequence, an explanation is offered in Section 6 for the double-walled structure sometimes observed in natural vortices. The experiments with no-slip boundary conditions reveal a very complicated flow structure in the vicinity of r = z = 0. The computed flow field is strongly reminiscent of that described by Benjamin (1962).