Surface modification of nanomaterials is the subject of numerous recent investigations. Quantitative characterisation of such modifications is of great theoretical and practical interest. As a first step, our attention is focussed on carbon nanotubes because of their unique morphology and physicochemical properties, having many potential advantages in nanotechnology, electronics, optics and other fields of material science. Surface modification or coating of the nanotubes is essential in several applications, using them as drug carriers, reinforcing component in polymeric matrices or hi-tech structural ceramics to create reactive surface groups or protection for efficient processing. Applying the simple planar approach to cylindrical-shaped samples, as known, leading to overestimated layer thickness values because the effective thickness of the layers (seen from the direction of analyser) varies from point to point along the convex surface of the tubes of essentially cylindrical geometry. In case of nanotubes, and any type of nano-objects, however, a further significant difference is that they have no ‘bulk-like’ core material because they are usually thin enough to be transparent by the photoelectrons evolving in the XPS measurements. In a step forward for quantitative characterisation, in this article, a special model was developed to calculate the thickness of the modified layer on nanotubes, taking into account that several rows of the tubes are randomly piled on each other. The applicability of the model was tested for quantitative characterisation on multiwall carbon nanotubes (MWCNT), which were treated in d.c.-biased RF N2 plasma for covalent attachment of nitrogen to their outer shells. This model will be implemented, and thus the calculations would be conveniently performed in the latest versions (from 7.0) of the XPS MultiQuant program. Copyright © 2012 John Wiley & Sons, Ltd.