The Polish men plan to ride their mini-tractors - with trailers and a top speed of 15 km/hour - all the way from the southern Polish town of Jaworzno to the basilica of St Therese in Lisieux.
The 1,700km (1,000 miles) trek is meant to mirror the film, which tells the story of an elderly man's journey on a lawnmower tractor from Iowa to Wisconsin to visit his sick brother.
The Polish men, accompanied by the priest who runs their homeless centre, said they wanted to prove themselves after battling with addiction and exclusion.
"While we have this time on earth, this is a time for reflection and this is what the movie is about," one of the men, Jacek Baczynski, said.
"The most important thing for me in this pilgrimage is to be there and pray... to be with family, people, for good relations, for love, for honesty, for meetings," another pilgrim, Kazimierz Lara, added.
Before they set off on Sunday, Lynch sent the men a good luck message for what he called a journey for "forgiveness, for love, for freedom and for peace".
The journey is expected to last several weeks.
(Reporting By Reuters Television, watch report here; Editing by Andrew Heavens)
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