Correlations between the local diameter and local radial elastic modulus in multiwalled carbon nanotubes (MWNTs) were investigated via ultrasonic force microscopy. Spatial cross-correlation analysis showed that local radial modulus variations were inversely correlated with local diameter gradients ("bamboo" structures) in MWNTs grown via chemical vapor deposition (CVD). In contrast, uniform MWNTs grown via arc discharge exhibited no such correlation, indicating that reductions of elastic modulus previously reported for CVD-grown MWNTs originated from increased defect density associated with local increases in diameter.