Recently there has been experimental evidence for structural transformations in single wall carbon nanotube bundles (SWCNTB) under pressure. We have performed ab initio electronic structure calculations on (10, 10) and (17, 0) SWCNTBs using the generalized gradient approximation for the exchange-correlation potential. When the cell shape is fixed to an hexagonal one, we find flattening of the nanotube walls in both the cases at low pressures. At higher pressures, the flattened walls buckle and ultimately cross-link. However, relaxation of the cell shape leads to a reversible first order transition of the (10, 10) SWCNTB lattice from near hexagonal to monoclinic. These results are discussed in the light of the available experimental results.