Process for additive manufacturing of at least one part. At least one layer of powder is deposited on a working surface using a layering device for distributing the powder mobile in translation along the surface and at least partly fusing the layer deposited using a beam of energy. The depositing and fusing steps are repeated in order to form the part by stacking of fused layers. The distribution component of the layering device is mobile in a direction substantially parallel to the direction of the length of each fused layer of the part. The depositing and fusing steps are repeated in order to form the part so that the length of the part extends along a direction substantially parallel to the stacking direction of the fused layers and so that the head of the part is oriented substantially perpendicular to the working surface.