We present results of first principles electronic structure calculations on (10,10) and (12,12) single wall carbon nanotube bundles under hydrostatic pressure using ultrasoft pseudopotential plane wave method and local density approximation for the exchange-correlation energy. It is found that the (10,10) bundles show a structural transformation of nanotubes from cylindrical to an oval shape accompanied by a transition from a near hexagonal to a monoclinic lattice. The (12,12) nanotubes are, however, commensurate with the underlying hexagonal lattice and there is only a polygonization to hexagonal shape of the nanotubes with increasing pressure accompanied by a reduction in the lattice constant. Similar results hold for zig-zag nanotubes also. This would explain the conflicting results obtained from experiments. Effects of pressure on the electronic structure are discussed. {\textcopyright} 2002 Elsevier Science B.V. All rights reserved.