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The element-based finite volume method (EbFVM) is well established in computational fluid dynamics; in the last decade, it has been extended to several areas of engineering and physics interest, such as electromagnetism, acoustics, and structural mechanics analysis with complex geometrical shapes. This paper describes the treatment of the conservative EbFVM approach for two-dimensional isotropic elastic–plastic rate-independent problems. In particular, we use plane strain and plane stress approaches upon incremental thermal and mechanical loads. In order to verify the performance of the EbFVM, numerical results are compared with a commercial simulator. Finally, from the present implementation and the comparisons performed, we can ensure that EbFVM makes accurate prediction as the traditional numerical approach commonly employed for the solution of mechanics problems.