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We present the results of axisymmetric and three-dimensional numerical simulations of the flow around a torus in the low Reynolds number regime [ 10 − 2 ; 3 × 10 3 ] and aspect-ratio 0 < Γ = 2 a / R ≤ 2 (core diameter over toroidal radius). It is shown that as Γ → 0 , consistent with intuition and the results from the literature, the flow tends to that of a two-dimensional circular cylinder while for Γ → 2 the flow is that around a bluff obstacle. It has been observed that in a small region of the R e – Γ phase space, the flow develops an axisymmetric recirculation detached from the torus and with a vorticity distribution that resembles the Hill vortex. In the range 0 < Γ ≤ 2 , several different regimes have been observed; the peculiarities of each regime are analyzed and, whenever possible, similarities and differences with other classical flows are discussed.