The transition to three-dimensional flow from the nominally two-dimensional Ka ́rma ́n vortex street in the wake of bluff bodies is a problem of fundamental importance as it marks the first step on the path towards fully developed turbulence. Here, this transition is studied in the wake of an elliptical cross-section using Floquet stability analysis. A number of modes of instability are identified as a function of the aspect ratio of the ellipse. Three-dimensional simulations confirm the importance of the identified instability modes.