This thesis describes measurements of the mechanical properties on the nanoscale. Three different mesoscopic tubular objects were studied: MoS2 nanotubes, carbon nanotubes and microtubules. The main goal was to investigate the interplay between the fine structure of these objects and their mechanical properties. Measurements were performed by elastically deforming tubes deposited on porous substrates with the tip of an atomic force microscope. The first experimental part describes the mechanical characterization of MoS2 nanotube bundles. Elastic deformation of MoS2 nanotube bundles can be modelled, in analogy with carbon nanotube bundles, using two elastic moduli: the Young's modulus and the shear modulus describing the weak intertube coupling. The measured Young's modulus of 120GPa has later been confirmed by theoretical modelling. It is in the range of commonly used engineering materials. The shear modulus corresponding to intertube sliding is an order of magnitude lower than in the case of carbon nanotube bundles. MoS2 nanotubes could therefore prove an interesting model for studying 1D and weakly coupled systems. They could also be interesting as AFM tips, especially for biological applications thanks to their sulphur-based chemistry. In the case of carbon nanotubes, the weak intertube coupling is a serious problem that has to be solved before they could be used as reinforcing fibers or building blocks of macroscopic objects. This problem was addressed in the second part of this thesis. Stable crosslinks were introduced into carbon nanotube bundles by irradiating them with electrons inside a TEM. AFM measurements performed in parallel with TEM observations show that the irradiation process is composed of two competing mechanisms: crosslinking, which is dominant at low exposures, and degradation of the crystalline structure followed by amorphization in the later stages of irradiation. Theoretical modelling shows that the crosslinks are most probably formed by interstitial carbon atoms. The third part of this thesis describes measurements of the mechanical properties of microtubules performed in the liquid environment. The bending modulus shows a pronounced temperature dependence, in good agreement with previously published data on the dynamic instability of microtubules. The shear and the Young's moduli were simultaneously measured, on two different temperatures, using a substrate prepared by electron beam lithography. These measurements have demonstrated that microtubules behave as strongly anisotropic cylinders. This is due to their structure, with large gaps separating neighboring protofilaments. The observed stiffening of microtubules on low temperatures (<15°C) is due to increasing interaction between the protofilaments. This manifests itself as a decrease of disassembly velocity, showing that the dynamic behavior of microtubules is reflected in their mechanical properties.