We take up the old problem of Calvert (J. Fluid Mech., vol. 29, 1967, pp. 691–703) concerning the wake of a cylinder inclined with respect to the flow direction, and consider it from the viewpoint of transition to turbulence. For cylinders placed perpendicular to the flow direction, we address the disagreement between numerical simulation of the ideal axisymmetric configuration and experimental observations. We demonstrate that for a disk (a cylinder of aspect ratio infinity) and a flat cylinder of aspect ratio ${\it\chi}=6$ (ratio of diameter to height), the numerically predicted transition scenario is limited to very small inclination angles and is thus difficult to test experimentally. For inclination angles of about $4^{\circ }$ and more, a joint numerical and experimental study shows that the experimentally observed scenario agrees qualitatively well with the results of numerical simulations. For the flat cylinder ${\it\chi}=6$, we obtain satisfactory agreement with regard to dependence of the critical Reynolds number ($\mathit{Re}$) of the onset of vortex shedding on the inclination angle. Both for infinitely flat disks and cylinders of aspect ratio ${\it\chi}=6$, a small inclination tends to promote vortex shedding, that is, to lower the instability threshold, whereas for inclination angles exceeding $20^{\circ }$ the opposite effect is exhibited. The Strouhal number of oscillations is found to be only very weakly dependent on the Reynolds number, and very good agreement is obtained between values reported by Calvert (J. Fluid Mech., vol. 29, 1967, pp. 691–703) at high Reynolds numbers and our simulations at $\mathit{Re}=250$. In contrast, we observe relatively poor agreement in Strouhal numbers when comparing the results of our numerical simulations and the data acquired from the experimental set-up described in this paper. Closer analysis shows that confidence can be placed in the numerical results because the discrepancy can be attributed to the influence of the support system of the flat cylinder. Suggestions for improvement of the experimental set-up are provided.