Materials at nano-scale are reported with distinguish mechanical, thermal, electrical, chemical, and other properties. Those properties have been envisioned to lead to "next industrial revolution", and enable a vast range of applications, such as sensors, electronics, energy storage/generation, and composite materials. It is essential to establish a comprehensive understanding of the properties to facilitate such wide utilizations. For instance, how much bending deformation can the bendable electronics bear? How the thermal conductivity can be effectively tailored to meet different requirements? In the author's research group, a series of research have been undertaken based on the experimental, numerical and theoretical studies. This talk aims to discuss the key findings of the mechanical behaviours/properties of different low-dimensional nanomaterials including the bending and vibrational properties of nanowires considering the impacts from surface effects and axial extension. Emphasis will also be put on the thermal conductivity of graphene-based materials. The understanding of those properties is expected to not only benefit the applications of nanomaterials but also shed lights on their design and manufacturing.