The grain shape and texture effects in aluminum alloys manufactured by selective laser melting are studied numerically in terms of micromechanical simulations. The method of step-by-step packing is adopted to generate the three-dimensional grain morphology typical for these materials. Crystal plasticity finite element simulations of uniaxial tension are performed for two models with random and cube-textured columnar grains inherent in selective laser melting. Comparative analysis of the computational results shows a substantial difference between the microscale stress and strain fields. The presence of cube-textured columnar grains provides more homogeneous stress-strain distributions inside the melt pools and unloads the adjacent regions of fine equiaxed grains, thus reducing high stress concentration in them.