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Due to high compatibility and solubility in human organism, special magnesium alloys are applied in bioengineering. Production of surgical threads to integration of tissue can be application of these types of alloys. This sort of application calls for fine wires with diameters from 0.1 to 0.9 mm. The warm drawing process in heated dies is proposed to increase the workability of the Mg alloys. The purpose of this paper is development and experimental validation of a mathematical model of a warm drawing process of wires made of MgCa0.8 and Ax30 alloys and determination of optimal parameters with the objective function defined as maximum of workability. The first part of investigation is focused on development of a numerical model, which is based on FE solution. The second part of paper is focused on experimental upsetting and tensile tests. Basing on these tests the flow stress and ductility models were obtained. The materials models are implemented into the Authors' FE code, which is dedicated to modelling of drawing processes. Experimental validation of model is based on thermo visual measurement of wire temperature during drawing.