The structural and electronic properties of BN(5, 5) and C(5, 5) nanotubes under pressure are studied by using first principles calculations. In our study range, BN(5, 5) undergoes obvious elliptical distortion, while for C(5, 5) the cross section first becomes an ellipse and then, under further pressure, is flattened. The band gap of BN(5, 5) decreases with increasing pressure, which is inverse to that of zinc blende BN, whereas for C(5, 5) the metallicity is always preserved under high pressure. The population of charge density indicates that intertube bonding is formed under pressure. We also find that BN(5, 5) may collapse, and a new polymer material based on C(5, 5) is formed by applying pressure.