Direct Manufacturing Laser Deposition is an innovative process that allows the manufacturing of fully densified parts with complex geometries. However, the development of this manufacturing technique is still limited, in particular due to the irregular surfaces. The purpose of this work is to better understand the complex mechanisms responsible for the delaterious surface based on numerical simulation results performed with the COMSOL Multiphysics® software. A first task was to validate the physical model and thermophysical properties. Thermohydraulic model with free surface include the surface tension effects and the deformation of the geometry is treated with a moving mesh based on ALE method. This predictive model has been transposed to the DMLD process incorporating the material addition. 2D modelling are performed to analyze the effect of process parameters on the shape of the melt pool, before modelling multilayer deposition and showing the surface irregularities. The study is later extended to a 3D case. The self-consistency of the model can predict the shape of deposits only from the operating parameters. In this approach, the substrate and the liquid bath are decoupled from the gaseous environment. The powder stream is treated separately with a 3D model calculating the trajectory of the particles. The prediction of different numerical models is validated through several experimental data.