Mechanical properties are of fundamental importance in materials science and engineering, and have been playing a great role in various materials applications in the human history. Measurements of mechanical properties of 2-dimensional (2D) materials, however, are particularly challenging. Although various types of 2D materials have been intensively explored in recent years, the investigation of their mechanical properties lags much behind that of other properties, leading to lots of open questions and challenges in this research field. In this review, we first introduce the nanoindentation technique with atomic force microscopy to measure the elastic properties of graphene and 2D transition metal dichalcogenides. Then we review the effect of defects on mechanical properties of 2D materials, including studies on naturally defective chemical-vapor-deposited and intentionally defective 2D materials. Lastly, we introduce a nano-electromechanical device, resonators, built on the basis of the excellent mechanical properties of 2D materials.