  We present our 12CO and 13CO mapping observations of SNR IC 443, interacting
with molecular clouds. It is the first large scale high resolution 13CO mapping
observation in the surrounding region. The morphologies of IC 443 in 12CO and
13CO are compared with the optical, infrared, Spitzer far-infrared, X-ray, and
neutral atomic gas (HI). We also make comparison and analysis in the kinemics,
using the date-cubes of 12CO, 13CO and HI, to help distinguish the complicated
gas motions in the shocked regions. Based on the work of Wang & Scoville
(1992), we present a new model to explain the origin of coexistence of shocks
with different speeds in a rather small region at the central clump B. We test
this new model via analyzing the HI and CO distributions in both velocity and
space domains. We also establish the relationship between the dissociation rate
of the shocked molecular gas and the shock velocity in this region. Finally, we
derive the optical depth of 12CO with the 13CO spectra in clump B, and discuss
the validity of the assumption of optically thin emission for the shocked 12CO.
