The structural complexity of vapor-grown carbon nanofibers means that they require a method that determines both their elastic properties and their corresponding morphology. A three-point bending test method was developed combining atomic force microscopy, transmission electron microscopy (TEM) and focused ion beam techniques to suspend individual nanofibers and measure their deflection coupled with accurate determinations of inner and outer diameters and morphology using high resolution TEM. This resulted in much improved accuracy and reproducibility of the measured values of the elastic modulus which ranged from 6 to 207 GPa. The data showed two distinct trends, with higher values of the modulus when the outer wall thickness of the nanofibers is larger than that of the inner wall, with the values decreasing with the overall wall thickness. These results suggest that the more ordered layers of the outer wall, closest to the inner wall, are mostly responsible for the nanofiber strength. For large nanofiber wall thicknesses of greater than 80 nm, the elastic modulus becomes independent of the thickness with a value of approximately 25 GPa. The results also demonstrate that this technique can be a standardized one for the detailed study of mechanical properties of nanofibers and their relationship to morphology.