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Claddings are used to protect areas of components that are exposed to particular chemical, physical or tribological stresses. The aim when developing a cladding process is to achieve a cladding with low waviness in order to reduce the amount of machining required. Computational models and FEA simulations can be used to determine process parameters for claddings with low rework including a prediction of the height and width of a single weld seam aswell as the development of welding strategies. In this paper empirical models describing the geometry of single weld seams on a substrate manufactured with a coaxial laser hot-wire cladding process are investigated for three steel wire materials and different welding parameters. The coordinates of surface points of the weld seams were detected using a laser scanning microscope and post-processed by a self-created script. In order to describe the cross sectional shape of the weld seams, the parameters of parabolic, cosinusiodal or circular arc model functions are derived from the surface data using a fitting algorithm. For the tested wire materials, an effect of the wire material on the shape of the weld seam was not observed. The investigations also show that regardless of the varied welding parameter set or wire material, a circular model function appears to be the most suitable model shape for describing the cross sectional weld seam geometry in coaxial laser metal deposition with hot-wire. The regression residua using a circular arc model function ranged from 18.9 $$\upmu$$ μ m to 34.6 $$\upmu$$ μ m, which indicates a good approximation.