The mechanical properties of magnetic materials are instrumental for the development of magnetoelastic theories 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 CrCl3 and CrI3, finding that the bilayers have Young’s moduli of 62.1 and 43.4 GPa, highest sustained strains of 6.49% and 6.09% and breaking strengths of 3.6 and 2.2 GPa, respectively. This portrays the outstanding plasticity of these materials that is qualitatively demonstrated in the bulk crystals. The current study will contribute to the applications of the 2D magnets in magnetostrictive and flexible devices.