The finite element method was employed for the numerical simulation of hetero-junction carbon nanotubes with all possible connection types and their corresponding fundamental homogeneous tubes. Then, atomically defective hetero-junction carbon nanotubes were modeled by introducing silicon impurities and vacant sites into their structures. Finally, the elastic and shear moduli of all the models were evaluated under tensile and torsional loads, based on the assumption of linear-elastic deformation of these nanomaterials. The results showed that armchair and zigzag carbon nanotubes have the highest Young's and shear moduli respectively, among homogeneous carbon nanotubes. The mechanical tests on the hetero-junction carbon nanotubes revealed that these nanotube types have lower moduli when compared to their fundamental tubes. It was clearly observed that armchair–armchair and zigzag–zigzag hetero-junction carbon nanotubes have the highest Young's modulus among the hetero-junction carbon nanotubes while the shear modulus peaks were seen in zigzag-zigzag models. On the other hand, the lowest values for the Young's and shear moduli of hetero-junction carbon nanotubes were obtained for the models with armchair-zigzag kinks. It was also discovered that the atomic defects in the structure of hetero-junction carbon nanotubes lead to a decrease in their Young's and shear moduli which seems to follow a linear trend and could be expressed by a mathematical relation in terms of the amount of the atomic defect in their structures which could be used for the prediction of the tensile and torsional strength of the atomically defective hetero-junction carbon nanotubes for their proper selection and applications in nanoindustry.