Flow-induced undamped, transverse vibrations of an elliptic cylinder at 45° incidence are investigated via stabilized space–time finite-element (FE) simulations in two-dimensions. The mass ratio of the oscillator is 10. Results are presented at Reynolds numbers (Re) of 100, 150, 200, and 250 over reduced speed varying from 1 to 10. Through implementation of the quasi-steady theory, it is found that motion of the cylinder is aerodynamically stable, i.e., purely vortex-induced and hence, galloping motion does not develop. A pair of synchronization regimes is identified in the neighborhood of reduced speeds 4 and 8, respectively. The vibrations are mildly hysteretic at Re = 200.