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The ZrCuSiAs materials have many interesting physical properties and have been extensively studied in recent decades. Recently, two Mn-based ZrCuSiAs-type pnictides, i.e. ThMnAsN and ThMnPN, have been synthesized in the experiment, which shows the anti-ferromagnetic properties. Motived by the experiment, we here perform a comprehensive investigation on their elastic, electronic, and magnetic properties by the density functional theory and Monte Carlo simulations. Our calculations show that ThMnAsN and ThMnPN are both antiferromagnetic semiconductors. The magnetic ground state of both materials is the C -type anti-ferromagnetism and their bandgaps are about 0.47 eV and 0.61 eV for ThMnAsN and ThMnPN, respectively. The Monte Carlo simulated Néel temperatures of ThMnAsN and ThMnPN are 57 K and 55 K, respectively. These results are well consistent with the experimental results. Our work not only reveals the physical essence of the two newly synthesized materials but also could help to the understanding of the magnetic behaviors of other ZrCuSiAs-type compounds. [ABSTRACT FROM AUTHOR]