We have investigated the quantum tunneling of damped flux lines of finite m
ass at T = 0 by extending our previous study of tunneling around T-0, the t
ransition temperature. In the case of a cubic pinning potential, considered
here, the action could be evaluated in a closed form for a flux line of fi
nite length. The tunneling rate reaches a finite limit at T = 0, although i
t is temperature dependent and exhibits a 1/T variation near T-0.