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In order to obtain high precision Al-Cu-Mg aluminium alloy isothermal extrusion parts with large extrusion ratio, it is necessary to accurately control the uniform exit temperature and deformation microstructure. Therefore, based on arbitrary Lagrange Eulerian (ALE) method, the isothermal extrusion process was simulated by ABAQUS finite element software. True stress-true strain curves of Al-Cu-Mg alloy at different temperature and strain rate were investigated by hot compression test. A new multi-physics coupling numerical model for isothermal extrusion process was established. The influence of extrusion speed, billet temperature and die temperature on the exit temperature and the distribution characteristics of the temperature field and strain rate field of extrusion products are studied; The isothermal extrusion was conducted to verify the model through the EBSD analysis and mechanical properties test of the deformed material. The results show that: 0.5mm/s extrusion speed can keep the exit temperature basically constant, in which the billet temperature is 450℃, cylinder temperature is 430℃, and die temperature is 400℃. After extrusion, the grains of the sample are significantly refined, and the preferred arrangement is to form < 111 > silk texture parallel to the extrusion direction, showing excellent tensile properties.