Abstract A computational approach to simulating the deformation response of additively manufactured aluminum alloys is presented. A three-dimensional microstructure with the grain geometry typical for aluminum alloys produced by selective laser melting is generated by the method of step-by-step packing. The grain behavior is described in terms of crystal plasticity with explicit consideration of the slip systems. A phenomenological equation is used to describe the critical resolved shear stress taking into account the grain cellular-dendritic substructure, grain boundary strengthening, and strain hardening. The microstructure-based constitutive model is used in simulations of quasistatic tension. In order to reduce the computational costs, quasistatic loading is simulated in terms of dynamics using an explicit time integration scheme which provides high numerical efficiency for solving non-linear problems. The calculation results for a polycrystalline model of additively manufactured aluminum alloy subjected to tension and shear along three different directions are presented to illustrate what might be obtained from the micromechanical simulations.