Using combination of scanning probe microscopy, ultrasonic vibrations and electrostatic interactions, we explore applications of 2D materials in the nanomechanical and nanoelectromechanical (NEMS) systems where the atomically thin layers are subjected to the flexural and normal stresses. We show that a new behaviour of 2DMs – a 2D buckling transition - that can significantly increase the sensitivity of NEMS sensors to applied stimuli, is directly linked to the local in-plane stresses in 2DM and its adhesion to the substrate. Our analysis of stress propagation through a few layer 2DM, a transversely isotropic material - indicate that it is directly governed by the ratio of the out-of-plane Young modulus and the in-plane shear modulus, explaining unusual recent experimental observation of “ultrasonic transparency” of few FLG and MoS2 such that allows to observe defects and structures deep under immediate surface of such materials.

Finally, we demonstrate that highly anisotropic properties of 2DMs allow exploration of local electrostatic interactions between the material and the substrate via nanomechanical actuation, thus revealing and mapping with nanoscale resolution the charges hidden under the layers of such materials.