The mechanical properties of individual multiwall boron nitride nanotubes (MWBNNTs) synthesized by a growth-vapor-trapping chemical vapor deposition method are investigated by a three-point bending technique via atomic force microscopy. Multiple locations on suspended tubes are probed in order to determine the boundary conditions of the supported tube ends. The bending moduli (EB) calculated for 20 tubes with diameters ranging from 18 to 58 nm confirm the exceptional mechanical properties of MWBNNTs, with an average EB of 760 ± 30 GPa. For the first time, the bending moduli of MWBNNTs are observed to increase with decreasing diameter, ranging from 100 ± 20 GPa to as high as 1800 ± 300 GPa. This diameter dependence is evaluated by Timoshenko beam theory. The Young's modulus and shear modulus were determined to be 1800 ± 300 and 7 ± 1 GPa, respectively, for a trimmed data set of 16 tubes. The low shear modulus of MWBNNTs is the reason for the detected diameter-dependent bending modulus and is likely due to the presence of interwall shearing between the crystalline and faceted helical nanotube structures of MWBNNTs.