The results of numerical experiments aimed at investigating the topology of the vortex structures shed by an oscillating foil of finite span are described. The motion of the foil and its geometry are chosen to mimic the tail of a fish using the carangiform swimming. The numerical results have been compared with the flow visualizations of Freymuth [J. Fluids Eng. 111, 217 (1989)] and those of von Ellenrieder et al. [J. Fluid Mech. 490, 129 (2003)]. The results show that a vortex ring is shed by the oscillating foil every half a cycle. The dynamics of the vortex rings depends on the Strouhal number $\mathrm{St}$ . For relatively small values of $\mathrm{St}$ , the interaction between adjacent rings is weak and they are mainly convected downstream by the free stream. On the other hand, for relatively large values of $\mathrm{St}$ , a strong interaction among adjacent rings takes place and the present results suggest the existence of reconnection phenomena, which create pairs of longitudinal counter-rotating vortices.