We report on measurements of the stiffness and breaking strength of monolayer MoS2, a new semiconducting analogue of graphene. Single and bilayer MoS2 is exfoliated from bulk and transferred to a substrate containing an array of microfabricated circular holes. The resulting suspended, free-standing membranes are deformed and eventually broken using an atomic force microscope. We find that the in-plane stiffness of monolayer MoS2 is 180 ± 60 Nm-1, corresponding to an effective Young’s modulus of 270 ± 100 GPa which is comparable to that of steel. Breaking occurs at an effective strain between 6-11% with the average breaking strength of 15 ± 3 Nm-1 (23GPa). The strength of strongest monolayer membranes is 11% of its Young’s modulus, corresponding to the upper theoretical limit which indicates that the material can be highly crystalline and almost defect-free. Our results show that monolayer MoS2 could be suitable for a variety of applications such as reinforcing elements in composites and for fabrication of flexible electronic devices.