This work reports a theoretical and numerical study of the parameters related to the process of laser powder deposition through a lateral nozzle. For this purpose, a 3D quasi-stationary finite element model was developed analytically and implemented numerically. The proposed model estimates the shape of the melt pool depending on the process parameters including scanning speed, powder mass flow, laser power, and physical properties. Also, phase transformations and physical properties (density, thermal conductivity, and specific heat) vary as function of temperature. In addition, thermo-capillary forces and their effect on fluid flow inside the melt pool are considered. The obtained set of equations coupled through the temperature variable was solved using COMSOL Multiphysics. The results are presented and compared with previously obtained experimental data, in which chromium powder was deposited, allowing validation of the model. Finally, variations at the melt pool geometry in terms of the operational parameters are analyzed. This model aims at estimation of melt pool geometry during laser powder deposition in time reasonably short to allow for predictable process control.