The high sensitivity of cavity ring-down spectroscopy has allowed us to observe a few perpendicular vibrational overtone transitions of HCN in the visible. These transitions display a sizable Herman-Wallis effect, that is an asymmetry in the relative intensities of the R and P branch lines. We have developed a theory for the first-order Herman-Wallis effect based upon using variational vibrational wave functions but treating the vibration-rotation interaction by first-order perturbation theory. In the specific case of perpendicular transitions, the first-order effect is dominated by Coriolis mixing of Sigma and Pi overtone states. We used the empirical energy surface by Carter, Mills, and Handy [J. Chem. Phys. 99, 4379 (1993)] restricted to the stretching degrees of freedom. Bending was included by multiplication of these stretching wave functions by harmonic wave functions of the bend. Vibrational transition moments were calculated using a polynomial surface fit to ab initio CCSD(T) dipole moment points by Botschwina et al. [Chem. Phys. 190, 345 (1995) and private communication]. We expected that this treatment would be accurate but the calculated Herman-Wallis effect is about one order of magnitude too large. To gain further insight into the poor agreement between theory and experiment, we have calculated the sensitivity of the Herman-Wallis coefficient and of the transition moment to the dipole and energy surface parameters. From this, it appears that the dipole surface, while producing accurate band intensities, could at the same time be inadequate to account for the Herman-Wallis effect. A similar possibility stands for the energy surface, which however is highly constrained by the requirement to fit the observed band origins.