A hard border on the island of Ireland can be avoided by using "established" technology and "modifying" existing arrangements, Brexiteer Tory MPs say.
The European Research Group said the issue had been allowed to "frame" the talks but need not block a trade deal.
They call for "effective co-operation" between Belfast and Dublin to address smuggling concerns and extra customs forms to be included in VAT returns.
The EU has insisted on a "backstop" to ensure the single market is protected.
Both the UK and the EU want to avoid a return to physical checks at the Northern Ireland border, but have yet to agree how this can be achieved.
The BBC's assistant political editor Norman Smith said the ERG's answer to the problem of the Irish border seemed to be that "there isn't really a problem".
He said the group was citing the example of the "invisible border" between Norway and Sweden as a precedent for how post-Brexit arrangements might work.
Speaking at the launch of the ERG's report in London, former Northern Ireland Secretary Owen Patterson said he and other MPs were trying to "help the European Union and the UK government" by "giving an answer" to a problem which has risked derailing the Brexit process.
What will become of the Irish border when the UK leaves the European Union?
He insisted there was "absolutely nothing new" in what the group was proposing because the solutions already exist to deliver "an ordered border".
He said there was already a tax, VAT, excise and currency border between Northern Ireland and the Republic of Ireland which was maintained by "administrative and technical tools".
This should continue after Brexit, he said, supplemented by a range of mechanisms to ensure customs checks are conducted away from the border, such as trusted trader schemes.
"We absolutely believe there is no need for new physical infrastructure at the border and it can be handled by current means," he said.
Two former Northern Ireland secretaries were among Tory MPs endorsing the proposals
The report acknowledges a range of new checks will be needed on goods passing across the 310 mile border between Northern Ireland and the Republic of Ireland after Brexit, including extra customs declarations and declarations of origin as well as sanitary, phytosanitary and product compliance procedures.
Among the proposals put forward in the document to deal with these are:
- Extra customs declarations should be incorporated into existing system of VAT returns
- Simplified customs procedures for the majority of cross-border trade
- Trusted trader-type schemes for large companies
- Equivalence of UK and EU regulations for agricultural produce
- Declaring the island of Ireland a Common Biosecurity Zone
The report concluded: "The proposals can be realised within the existing legal and operational frameworks of the UK and EU, based on the mutual trust on which regular trade depends.
"They do nothing to alter the constitutional position of Northern Ireland and do not violate the principle of consent of the enshrined in the Belfast Agreement."