Raman spectroscopy is a technique widely used to study the vibrational modes of carbon nanotubes. The low-frequency Radial Breathing Modes (RBMs) are frequently used to characterize carbon nanotube samples. We report a Raman spectroscopic study on the strain-induced intensity variations of the RBMs of Single-Wall Carbon Nanotubes (SWNTs) in epoxy/SWNT composites. The RBM intensities have been found to vary significantly over a range of strain between -0.3% and 0.7%. The trend (increase or decrease) as well as the magnitudes of the intensity variation depends on the nanotube diameter and its chirality. Using tight-binding calculations, we have shown that these intensity variations can be explained entirely by resonance theory. Electronic density of states calculations confirm that the energy separation between the Van Hove singularities shifts with strain. The nanotubes are thus moved closer or further away from resonance, causing the intensity variations. It is demonstrated that through the use of resonance theory, a tentative chirality can be assigned to each type of SWNT from knowledge of its RBM position and the effect of strain upon the RBM intensity, thus determining its entire structure.