When a surface of a radiation-absorbing material is illuminated by a sufficiently intense radiation, the gas ablated from the surface produces reactive a force causing an acceleration of the initial matter and setting a stage for instabilities of the Rayleigh–Taylor type. New effects associated with the non-normal incidence of the radiation are analysed. It has been shown that, at large enough tilt, the instability becomes significantly faster than in the `normal' case and unstable modes acquire finite phase velocity along the surface. The most unstable perturbations are rolls whose orientation depends on the angular distribution of radiation. These results are of interest for laboratory studies of ablation fronts and for the theory of photoevaporation fronts in astrophysics.