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Many numerical weather prediction models employ terrain‐following vertical coordinates. As a consequence, over orography, flat tops of stratus clouds are intersected by the vertical coordinate surfaces. We conduct idealised two‐dimensional simulations of a stratus cloud with the COSMO model to study the effect of such sloping vertical coordinate surfaces. The evolution of the stratus cloud above a flat surface within a horizontally homogeneous atmosphere serves as a reference. During night‐time, the cloud thickens, driven by radiative cooling at the cloud top. Adding a sinusoidal perturbation to the vertical coordinate surfaces reduces the growth of the stratus cloud. With strong perturbations, the cloud starts to dissipate. The physical processes in the two simulations are identical, hence this behaviour is purely driven by numerical diffusion. The cloud is similarly thinned when sinusoidal orographic features are introduced. The reduction depends on the amplitude and wavelength of the perturbations and hills. Increasing the horizontal resolution partly mitigates the numerical diffusion. However, this is a very costly measure for an operational weather model. We suggest conducting further research on a new vertical coordinate with additional local smoothing of the orographic signal. [ABSTRACT FROM AUTHOR]