Friction stir back extrusion (FSBE) is used to produce brass wires and then, Numerical modeling is developed to simulate the FSBE of brass based on the Coupled Eulerian-Lagrangian technique (CEL) and verified by experiments. Next, the effects of FSBE parameters such as tool rotational and plunging speed on the strain and temperature distributions, microstructure, and patterns of material flow are studied. The results show that, the highest temperature and strain occurs near the tool/workpiece interface, but in a further distance from the tool axis. Additionally, in the cross section of a FSBE wire, the microstructure is finer in the periphery of the sample. A higher rotational speed or a lower plunging speed results in a coarser microstructure. The material flow pattern during the process is conical helix, and does not change meaningfully by the process parameters. The points at the further distance from the tool axis, along with an upward movement, experience an inward spiral movement which is amplified by higher rotational speed. However, the materials very near the tool axis almost take an upward movement and endure a very lower strain.