Despite all the recent advances in the development of three-dimensional (3-D) concrete printing (3DCP), this technology still has many unresolved problems. In most of the completed projects with the application of 3DCP, the focus was mainly on mastering the printing of vertical walls, while horizontal structural elements were produced with conventional methods—that is, using formwork, which reduces the level of technology automation, or using prefabricated elements, which makes the construction dependent on their availability and supply. In this contribution, the authors propose new methods of manufacturing slabs and beams directly on site by extruding concrete onto a textile reinforcement mesh laid on a flat surface. Specimens obtained from a slab produced following this method were used for mechanical testing and investigation of the concrete-reinforcement interface zone. Finally, as proof of the feasibility of the proposed approach, a demonstrator representing a full-scale door lintel was manufactured.