The present research was aimed at lowering the deformation temperature by applying cover tube casing (CTC) to AZ31 magnesium alloy samples subjected to equal channel angular pressing (ECAP) without triggering surface defects and/or fracture. The Cockcroft-Latham (C & L) fracture model was incorporated into finite element simulation and the critical values for a fracture to occur were determined. The fracture was predicted for the samples deformed at 150, 175, and 200 °C without CTC and with CTC having thicknesses of 1 and 4 mm. The predictions of the model were verified with experimental data. It was found that the workability of AZ31 increased with increasing CTC thickness, as a result of a reduction in the maximum principal stress at the top surface, a uniform distribution of strains, and an increase in the critical damage. In practice, the use of CTC led to the possibility of a reduction in deformation temperature by 25 °C. A sound product with a homogeneous grain structure and a mean grain size of 11 μm was achieved at 175 °C. Thus, the ECAP working window for the alloy was enlarged with accompanying benefits in energy consumption, tooling life, and manufacturing costs.