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The mechanical properties of magnetic materials are instrumental for the development of the magnetoelastic theory and the optimization of strain-modulated magnetic devices. In particular, two-dimensional (2D) magnets hold promise to enlarge these concepts into the realm of low-dimensional physics and ultrathin devices. However, no experimental study on the intrinsic mechanical properties of the archetypal 2D magnet family of the chromium trihalides has thus far been performed. Here, we report the room temperature layer-dependent mechanical properties of atomically thin CrI3 and CrCl3, finding that bilayers of CrI3 and CrCl3 have Young's moduli of 62.1 GPa and 43.4 GPa, with the highest sustained strain of 6.09% and 6.49% and breaking strengths of 3.6 GPa and 2.2 GPa, respectively. Both the elasticity and strength of the two materials decrease with increased thickness, which is attributed to a weak interlayer interaction that enables interlayer sliding under low levels of applied load. The mechanical properties observed in the few-layer chromium trihalide crystals provide evidence of outstanding plasticity in these materials, which is qualitatively demonstrated in their bulk counterparts. This study will contribute to various applications of the van der Waals magnetic materials, especially for their use in magnetostrictive and flexible devices., Comment: Main text and supplementary information