We present a survey of molecular gas in the J = 1 --> 0 transition of (CO)-
C-12 towards the IRAS Vela Shell. The shell, previously identified from IRA
S maps, is a ring-like structure seen in the region of the Gum Nebula. We c
onfirm the presence of molecular gas associated with some of the infrared p
oint sources seen along the shell. We have studied the morphology and kinem
atics of the gas and conclude that the shell is expanding at the rate of si
milar to 13 km s(-1) from a common center. We go on to include in this stud
y the Southern Dark Clouds seen in the region. The distribution and motion
of these objects firmly identify them as being part of the shell of molecul
ar gas. Estimates of the mass of gas involved in this expansion reveal that
the shell is a massive object comparable to a GMC. From the expansion and
various other signatures like the presence of bright-rimmed clouds with hea
d-tail morphology, clumpy distribution of the gas etc., we conjecture that
the molecular gas we have detected is the remnant of a GMC in the process o
f being disrupted and swept outwards through the influence of a central OB
association, itself born of the parent cloud.