To prevent a part of a container which is not necessary to heat from being heated as much as possible when a cap seal is to be heat-shrunk thereby suppressing an increase in temperature of contents to prevent degradation in quality.

The cap seal attaching method for heat-shrinking a heat- shrinkable tubular cap seal 6 fitted over a mouth 2a of a container 2 filled with contents such as milk comprises steps of spouting steam from a steam spout means 8 over the cap seal 6 to have it heat-shrunk while the container 2 is carried by a conveyer 4 and passed through a shrink tunnel 5, spouting cooling water from a cooling water spout means 12 over a barrel 2b of the container 2, and thereafter spouting cooling water from a cooling water spout means 13 over the container 2 and the cap seal 6 which has been shrunk.