Whether a particle sticks or rebounds upon impact on a flat surface is rather well understood for normal incidence. In this case the fate of the particle (stuck or bounced) is determined by a criterion expressed in terms of the normal impact velocity being larger than a "critical velocity". The "critical velocity" is in principle function of physical and material properties of the particle-surface combination and it can be measured in well-defined experiments. In addition, theoretical estimates for it can be made depending on the prevailing particle-surface contact mechanics. Oblique impact is not as well characterized and a simple particle sticking/rebounding criterion analogous to that for normal impact is not available. In the present study, we introduce and test the validity of such a criterion. The new criterion is cast in terms of a "critical impact angle" of incidence, beyond which no particle deposition is possible, irrespective of the value of the normal velocity. For elastic-frictional-adhesive contacts the criterion can be expressed in terms of the friction coefficient and the effective Young and Shear moduli of the particle-surface combination. The sticking/rebound criteria for normal and oblique incidence in conjunction with particle trajectory calculations are applied to analyze several sets of experimental data in the literature and they are shown to explain very well the sticking fraction of inertially impacting aerosol particles on cylindrical and spherical collectors, over the entire range of Stokes numbers. (C) 2005 Elsevier Ltd. All rights reserved.