Magnesium sheet alloys possess limited plastic formability at room temperature but their formability is substantially improved at elevated temperatures and optimum strain rates. In the present paper, three different types of failure criteria, namely, strain-based, stress-based, and work-based criteria, are compared for their applicability to warm press forming of magnesium sheet alloys. Warm deep-drawing experiments were conducted on AZ31 alloy sheet, and the results were used to assess the strength and weakness of the failure criteria.