Investigation of influence of TiN thin film morphology on deformation inhomogeneities is an overall subject of the research. Numerical modelling approach that was selected for the study is based on the digital material representation concept, which gives an opportunity to directly replicate columnar microstructure morphology of an investigated thin film. Particular attention in this paper is put on the discussion of the influence of cellular automata neighbourhood on thin-film digital morphologies and their further deformation behaviour. Additionally, an evaluation of representativeness aspects of the digital models, in particular, the analysis of the influence of a number of columns, their dimensions and variations in their properties on the material behaviour during compression tests is also presented. The non-periodic boundary conditions are assumed during the investigation. Obtained data in the form of equivalent stress distributions as well as homogenized stress-strain curves from analyzed case studies are presented and discussed within the paper.