Tetra−Penta−Deca−Hexa graphene (TPDH) is a new two-dimensional (2D) carbon allotrope with attractive electronic and mechanical properties. It is composed of tetragonal, pentagonal, decagonal and hexagonal carbon rings. When TPDH graphene is sliced into quasi-one-dimensional (1D) structures such as nanoribbons, it exhibits a range of behaviors, from semimetallic to semiconducting. An alternative approach to achieving these desirable electronic properties (electronic confinement and nonzero electronic band gap) is the creation of nanotubes (TPDH-NTs). In the present work, we carried out a comprehensive study of TPDH-NTs combining Density Functional Theory (DFT) and classical reactive Molecular Dynamics (MD). Our results show structural stability and a chiral dependence on the mechanical properties. Similarly to standard carbon nanotubes, TPDH-NT can be metallic or semiconductor. MD results show Young's modulus values exceeding 700 GPa, except for nanotubes with very small radii. However, certain chiral TPDH-NTs (n, m) display values both below and above 700 GPa, particularly for those with small radii. Analysis of the evolution of von Mises stress and the distribution of C−C bond angles and lengths throughout the stress−strain process indicates the important role of tetragonal, pentagonal, and hexagonal rings for the mechanical response of TPDH-NTs. Tetragonal and pentagonal rings provide a rigid mechanical framework for TPDH-NTs (n, 0), whereas pentagonal and hexagonal rings provide TPDH-NTs (0, n) with greater flexibility.