The study used Density Functional Theory to simulate the properties of single-walled and double-walled boron nitride nanotubes. The cohesive energy calculations suggest that double-walled nanotubes are more stable than single-walled nanotubes. Double-walled nanotubes have a narrower bandgap than single-walled nanotubes. The smaller diameter of the nanotubes reduces available energy for vibrational modes. Double-walled nanotubes have larger Young’s modulus, shear modulus, and bulk modulus than single-walled nanotubes. Both single-walled and double-walled nanotubes perform like auxetic materials in some directions. The group velocity of acoustic phonons in SWBNNTs (6, 0) is higher than in SWBNNTs (12, 0).