The cabinet is split over how to manage customs arrangements with the EU.
Brexiteers such as Boris Johnson are against Mrs May's preferred option of a "customs partnership", which is backed by Remain-voting ministers.
Mr Johnson's preferred model relies on technology to minimise customs checks. The EU has expressed doubts about whether either option would work.
The prime minister has said further work is needed to come up with a solution that will deliver on her promise of frictionless trade without the need for a hard border between Northern Ireland and the Republic.
She needs to find a solution to present to the EU at the next round of Brexit talks, with just five months left to get an agreement on post-Brexit trade, so it can be ratified before Britain leaves in March next year.
Mr Johnson and Chancellor Philip Hammond - who are thought to have been at loggerheads over the customs issue - will not play a role in either of the two working groups.
One group will consider a "customs partnership" whereby the UK would collect tariffs on behalf of the EU, but would remove the need for new checks at the border.
The other group will look at "maximum facilitation" - a solution based on using technology to minimise the need for customs checks after Brexit.
Looking at the customs partnership proposal will be two Brexiteers - International Trade Secretary Liam Fox and Environment Secretary Michael Gove - and Remainer Cabinet Office minister David Lidington.
All EU members are part of the customs union which means there are no tariffs on goods transported between member states.
Labour is in favour of setting up a new customs union with the EU after Brexit, something it says is backed by the trade unions and industry body the CBI.
The customs partnership proposal
The UK would collect tariffs set by the EU customs union on goods coming into the UK on behalf of the EU.
If those goods didn't leave the UK and UK tariffs on them were lower, companies could then claim back the difference.
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