jats:pFlow through a sinuous stenosis with varying degrees of non-axisymmetric shape variations and at Reynolds number ranging from 250 to 750 is investigated using direct numerical simulation (DNS) and global linear stability analysis. At low Reynolds numbers (Re &lt; 390), the flow is always steady and symmetric for an axisymmetric geometry. Two steady state solutions are obtained when the Reynolds number is increased: a symmetric steady state and an eccentric, non-axisymmetric steady state. Either one can be obtained in the DNS depending on the initial condition. A linear global stability analysis around the symmetric and non-axisymmetric steady state reveals that both flows are linearly stable for the same Reynolds number, showing that the first bifurcation from symmetry to antisymmetry is subcritical. When the Reynolds number is increased further, the symmetric state becomes linearly unstable to an eigenmode, which drives the flow towards the non-axisymmetric state. The symmetric state remains steady up to Re = 713, while the non-axisymmetric state displays regimes of periodic oscillations for Re ≥ 417 and intermittency for Re ≳ 525. Further, an offset of the stenosis throat is introduced through the eccentricity parameter E. When eccentricity is increased from zero to only 0.3% of the pipe diameter, the bifurcation Reynolds number decreases by more than 50%, showing that it is highly sensitive to non-axisymmetric shape variations. Based on the resulting bifurcation map and its dependency on E, we resolve the discrepancies between previous experimental and computational studies. We also present excellent agreement between our numerical results and previous experimental results.</jats:p>