The elastic properties of single-walled carbon nanotube heterojunctions were investigated using conventional tensile, bending and torsion tests. A three-dimensional finite element model was built in order to describe the elastic behaviour of cone heterojunctions (armchair–armchair and zigzag–zigzag). This comprehensive systematic study, to evaluate the tensile, bending and torsional rigidities of heterojunctions, enabled the formulation analytical methods for easy assessment of the elastic properties of heterojunctions using a wide range of their geometrical parameters.