Abstract The molecular distribution toward the whole extent of the Vela SNR has been obtained at a linear resolution of 0.15 pc in 12CO ($J = 1 \hbox{--} 0$) emission with the NANTEN telescope. The CO distribution is generally anti-correlated with the SNR. The X-ray distribution has a sharp boundary toward the CO clouds, especially in the east, suggesting an interaction between them. There is only weak CO emission in the west, and the X-ray emission extends smoothly toward this direction. This indicates that the absence of dense gas probably allowed hot gas to escape freely. The CO clouds are highly filamentary, exhibiting a spatial correlation with regions of optical shocked features on a large scale. In the north of the SNR, enhanced X-ray emission is found toward network-like optical filaments. We suggest that this enhancement is due to the evaporation of molecular gas by shock heating caused by the interaction between the blast wave and the molecular gas. Comparisons with a few simple theoretical models of SNR evolution and expansion indicate that the clouds are mostly pre-existent, are being accelerated, and are evaporating now.