Johnson told the Sunday Times that May's Brexit plan won't work, particularly proposals that would require Britain and the EU to collect each other's tariffs.
Johnson said it's "entirely preposterous. The idea that we could ask customs officers in Dubrovnik and Santander to charge British-only tariffs is deranged, and nobody thinks it can work."
May's plan would keep Britain in the EU's single market for goods, while letting the country write its own rules on services and strike free-trade deals with third parties. EU leaders have rejected that idea, saying the UK wants the benefits of membership without accepting its responsibilities.
Meanwhile, May called on her party on Sunday to unite behind her Brexit plan, making a direct appeal to critics by saying their desire for a free trade deal was at the heart of her own proposals.
"My message to my party is let's come together and get the best deal for Britain," May told the BBC in the central English city of Birmingham.
"At the heart of the Chequers plan is a free trade deal, a free trade area and frictionless trade ... Chequers at the moment is the only plan on the table that delivers on the Brexit vote ... and also delivers for the people of Northern Ireland."
May has shown little sign of shifting away from her Chequers plan, named after her country residence where she hashed out an agreement on Brexit with her ministers in July, despite growing criticism that her proposals offer the worst of all worlds.
AP and Reuters contributed to this story.