Hollow tubular tissues and organs of our body have various functions : gastrointestinal (esophagus), respiratory (trachea), vascular (veins, arteries). A panel of pathologies is associated with each of these tissues and therapeutic interventions, surgery or replacement may be necessary. A precise knowledge of the mechanical properties of these tissues is thus required in order to understand their functioning in native conditions, to be able to elaborate some prostheses, or to design appropriate surgical training tools. These tissues may undergo expansions or contractions (peristalsis) and are exposed to internal pressures. The wall of tubular organs is organized in different layers, and each layer consists of various cell types and extra-cellular matrix, depending on the physiological functions that the organ has to fulfil. This yields anisotropic and compliant structures. In inflation experiments, the linear elasticity approach is acceptable as long as the organ's inflation remains moderate. In this paper, elasticity laws are revisited and supplemented in order to show that, coupled with modern experimental characterization tools, they provide useful informations (compliances, directional Young moduli, Poisson ratios) for the design of artificial tubular organs. The importance of a precise determination of the wall thickness and of its evolution during inflation is pointed out.