The unique features of axial, torsional, transverse and radial breathing vibrations are captured for armchair and zigzag singlewalled boron nitride nanotubes (BNNTs) based on molecular mechanics simulations and continuum mechanics theories. Equivalent Young’s modulus 1 TPa and shear modulus 0.4 TPa are obtained independent of the chirality of BNNTs. In particular, a distorted optimized structure is observed for the first time for BNNTs with sufficiently large diameter and length. It is found that the deformed structures result in behaviours of BNNTs deviating from those of classical columns/beams. Such symmetry-breaking could also exert significant impacts on the structural instability (buckling) and electronic properties of BNNTs that are sensitive to the structural symmetry.