In this study, laser metal fusion with feedstock wire is addressed. We investigated how various process parameters affect the fraction of beam energy that is absorbed by the wire and the workpiece and the metal transfer from the feedstock wire to the melt pool. To perform this research, a thermo-fluid dynamic model with tracking of free surface deformation was developed to include the feeding of a solid wire and predict its melting. The fraction of beam energy absorbed by the metal was modeled as a function of local surface curvature and temperature, accounting for multiple Fresnel reflections and absorptions. The model was applied to Titanium alloy (Ti-6Al-4V) with a 1.07 μm laser and a process in conduction mode. Experiments at various wire feeding rates were conducted to evaluate the model’s ability to predict the process and a good agreement was obtained. The different parameters studied were the beam angular position, the wire angular position, the wire feed rate, and the beam-wire offset. The analysis of the simulation results gave a detailed physical understanding of the laser energy use. It highlighted that thermocapillary and Rayleigh-Plateau instabilities can contribute to the transition from continuous to drop metal transfer mode. Damping these instabilities might thus allow using a wider process window.