This paper presents a new computational framework to describe the evolution of grain structure during metal additive manufacturing and to simulate an inelastic deformation of the additively manufactured material, taking into account the grain structure explicitly. A combined effect of grain structure and loading conditions on the evolution of the stress-strain state in additively manufactured specimens is investigated. The results of the research highlight the need to account for the realistic microstructure, to properly describe the mechanical behaviour of additively manufactured specimens and parts. This is part of a thematic issue on Small Scale Mechanics - EUROMAT.