Purpose The purpose of this paper is to develop a numerical approach inspired by Geometrical Product Specifications (GPS) standards for the assessment of geometrical defects appearing during Additive Manufacturing (AM) by Laser Beam Melting (LBM). Design/methodology/approach The study is based on finite element (FE) simulations of thermal distortions, then an assessment of flatness defects (warping induced by the high-residual stresses appearing during the manufacturing) from the deformed surfaces provided by simulation, and finally the correction of the calculated flatness defects from preliminary comparison between simulated and experimental data. Findings For an elementary geometrical feature (a wall), it was possible to identify the variation in the flatness defect as a function of the dimensions. For a complex geometry exhibiting a significant flatness defect, it was possible to improve the geometric quality using the numerical tool. Research limitations/implications To the best of the author’s knowledge, this work is the first attempt using a numerical approach inspired by GPS standards to identify variations in thermal distortions caused by LBM, which is an initial step toward optimization. This paper is mainly focused on flatness defect assessment, even though the approach is potentially applicable for all types of geometrical defects (shape, orientation or position defects). Practical implications The study opens prospects for the optimization of complex parts elaborated using LBM, based on the minimization of the geometric defects caused by thermal distortions. Social implications The prospects in terms of shape optimization will extend the potential to benefit from the new possibilities offered by LBM additive manufacturing. Originality/value Unlike the usual approach, the proposed methodology does not require any artifacts or comparisons with the computer-aided-design (CAD) model for geometrical distortion assessment. The present approach opens up the possibility of performing metrology from FE simulation results, which is particularly promising in the AM field.