Using DNS, we investigate the dynamics in the wake of a circular disk of aspect ratio χ = d/w = 3(where d is the diameter and w the thickness) embedded in a uniform flow of magnitude U0 perpendicular to its symmetry axis. As the Reynolds number Re = U0d/ν is increased, the flow is shown to experience an original series of bifurcations leading to chaos. The range Re ∈ [150, 218] is analysed in detail. In this range, five different non-axisymmetric regimes are successively encountered, including states similar to those previously identified in the flow past a sphere or an infinitely thin disk, as well as a new regime characterised by the presence of two distinct frequencies. A theoretical model based on the theory of mode interaction with symmetries, previously introduced to explain the bifurcations in the flow past a sphere or an infinitely thin disk (Fabre et al. in Phys Fluids 20:051702, 2008), is shown to explain correctly all these results. Higher values of the Reynolds number, up to 270, are also considered. Results indicate that the flow encounters at least four additional bifurcations before reaching a chaotic state.