Double-walled metal pipes are important components for heat exchange and liquid transportation. They can be manufactured by mechanical drawing of two concentric pipes. In this work, a mechanical model is developed to analyze the stress state evolution during the manufacturing process, and the criterion for forming the double-walled pipe was given under the ideal elastoplastic and thick-wall assumptions. The model also encompasses the results deduced under the thin-wall assumption. Numerical simulations confirmed that the accuracy of the analytical model was within 5%. The application on actual steel materials with various parameters varied, including the wall thickness and initial gap, was analyzed. This work can provide theoretical support to industrial manufacturing procedures and help to reduce costs by eliminating required test procedures.