In this paper the mechanical properties of carbon nanotubes are discussed in connection with the possibility to use them for the construction of a space elevator. From the fundamental information about the structure of a carbon nanotube and the chemical bond between carbon atoms, Young's modulus and the ultimate tensile strength are estimated. For this calculation only simple high school physics is necessary. The results, the same as known from experimental data, show that carbon nanotubes could be, at least hypothetically, a possible material for construction of a space elevator cable.