The miners have been trapped since Aug 5 when a tunnel collapsed at the mine, located about 700 km north of Chilean capital Santiago. Thirtythree miners face up to four months in isolation as engineers drill a narrow escape shaft.
A minister's cheeks flushed when he was shown one of the jokes and he was too embarrassed to read it out, The Sun reported Saturday.
Relatives are sending jokes to the miners to lift their spirits.
The church sent down rosaries blessed by the Pope Friday. Chilean Cardinal Francisco Javier Errazuriz held a mass at the mine.