Peptide nanostructures present a wide range of opportunities for applications in biomedicine and bionanotechnology; hence experimental and theoretical studies aiming at determination of thermo-mechanical stability of peptide-based nanostructures are critical for the design and development of their technological applications. Here, we present a homogeneous deformation method combined with the finite elasticity theory and molecular dynamics simulations (MD) for the calculation of second-order anisotropic elastic constants for a membrane model made up of self-assembled cyclic peptide nanotubes. We have computed the values of all anisotropic elastic constants at 300 K. The value of the engineering Young's modulus (in the z direction) is 19.6 GPa. We observed a yield behavior in the z direction for a strain value of 6%. Furthermore, we also report calculated heat capacity, thermal expansion coefficient and isothermal compressibility of the system under study.