Most of the papers devoted to the FDM Additive Manufacturing Process concern the thermal phenomena occurring during the deposit of the successive layers of molten polymer on a substrate. In this paper we focus our analysis on the mechanical phenomena arising in the deposit nozzle and between the nozzle and the substrate. Analytical calculations allow deriving relationships between the polymer viscosity, the processing conditions (flow rate, velocity of the nozzle, the gap between the nozzle and the substrate) the dimensions and the geometry of the nozzle, and the resulting shape of the deposited layer (thickness and width) as well as the pressure distribution between nozzle and substrate. The pressure distribution will influence adhesion between the successive layers as well as the porosity of the part and the possible defect occurrence. Modifying the shape of the nozzle will influence the dimensions of the deposited layer as well as the pressure distribution. Comparison with 3D REM3D finite element computations will be presented.