In this study, an Al-Mg alloy sheet (AA5052 series) is subjected to a newly modified severe plastic deformation (SPD) process named as constrained groove pressing (CGP). Two different routes of classical and cross are employed and compared for the first time in this research. Each pass of the classical route process is including four subsequent corrugating and straightening stages with a 180-degree rotation between them and imparted an equivalent plastic strain of ?1.16. Meanwhile, the number of stages for cross route process is eight as well as a 90-degree rotation between the consequent passes and leads to the imposing of a strain ?2.32. These processes are implemented up to two passes on the examined Al-Mg alloy. As the main objective of the present research, strain and hardness distributions along the main three directions (rolling, transverse, and normal) and from different sections (surface and thickness) during different stages and passes of classical and cross routes are simulated by using 3D non-linear finite element (FE) modeling. ABAQUS/Explicit software is used for this purpose. The effects of classical and cross routes on the strain distributions and homogeneities as well as the hardness profiles during different stages of the CGP process are compared. Also, the simulated results are validated with the experimentally measured hardness data and in accordance some good agreements noticed. Finally, a hardness-tensile strength relationship is established based on the microstructural details and imposed strain contours to predict the tensile strength of processed Al-Mg alloy with the classical and cross routes by the implementation of FE simulation.