Cells and subcellular organelles undergo significant morphological changes in their life course, which requires crucial bending on their membranes. Therefore, characterizing the elastic properties of membranes and their deformation behavior has gained significant attention in the past decades. Researchers often use vesicles as model systems to study the mechanical properties of membranes because vesicles form the frame of various sub-cellular organelles such as lysosomes, endosomes, exosomes, as well as the lipid envelope of viruses. However, due to technological limitations, researchers have to use microscale vesicles hundreds of times larger than their naturally-occurring counterparts that are sub-micron in size. Since length-scale plays a crucial role in mechanical properties of vesicles, microscale vesicles are not a reliable model system for many biologically-relevant processes. The main objective of this research is to develop a novel analytical platform that enables measuring the elasticity of nanoscale vesicles. In order to characterize nanoscale vesicles, we employ a solid-state nanopores and an electric field to form a local strong field inside the pore. Nanoscale vesicles, dispersed in an ionic solution, are then allowed to translocate through the pore, where they undergo a strong DC pulse. Such a strong DC pulse can deform the nanoscale vesicle due to the well-known phenomenon called electrodeformation. By measuring the ionic current through the pore and blockade events caused by vesicle translocation, we characterize the morphology of the translocating vesicle. Hence, electrodeformation in nanopores allows characterizing force-deformation properties of nanoscale vesicles. In this dissertation, we focus on proof-of-the-concept experiments and particularly investigate the electrodeformation of nanoscale vesicles of varied mechanical properties. First, we show that elastic properties of liposomes can be characterized from their respective resistive pulse measurements. Then, we will use the theories of vesicle electrodeformation and translocation through nanopores to model the morphology of deformed liposomes inside nanopores. Finally, we will use this model along with resistive pulse measurements of human immunodeficiency (HIV) viruses to demonstrate the application of our platform for characterizing mechanical elasticity of viruses at nanoscale. Collectively, our results suggest that electrodeformation in solid-state nanopores can be used to describe the deformation behavior of nanoscale vesicles.