The 11 options published today also include a new road to bypass the notorious pass to the north.
A “preferred route option” is due to be chosen next spring, Transport Scotland said.
The shortlist includes a 2.4-mile-long bridge or tunnel from Cloch Point, south of Gourock, to Dunoon.
An even more ambitious option would involve a 1.6-mile-long bridge or tunnel across the Clyde between West Kilbride in North Ayrshire and Little Cumbrae, and another one of similar length between the island and Bute.
However, this would “provide significant technical challenges” because the channels are used by large ships and submarines.
A third bridge or tunnel, 0.3-mile-long, would link Bute to the Cowal peninsula south of Dunoon, or further to the west.
Another option would involve a new road through Glen Kinglas to the north of the A83, with a further one seeing a new road through Glen Fyne, slightly further north still.
Further options include a new road close to the current A83, and upgrading existing roads with a new bridge or tunnel across Loch Long west of Garelochhead.
Another option would include a new bridge or tunnel across Loch Fyne, east of Lochgilphead.
New bridges or tunnels between Rhu, near Helensburgh and the Cowal peninsula north of Dunoon across the Gare Loch and Loch Long via the Roseneath peninsula are also on the list.
Transport secretary Michael Matheson said: “Following the recent landslips at the A83 Rest and Be Thankful, I understand the frustration and disruption that these bring for local communities and road users.
“While our previous and on-going investment in catch pits has helped keep the road open for an estimated 48 days when it would otherwise have closed, I realise people are looking for a long-term solution to dealing with landslips at the site and we are committed to delivering one.
“Transport Scotland is now taking forward the project development and assessment work required to deliver an alternative infrastructure solution to the existing A83, in parallel with the second Strategic Transport Projects Review.
“We are committed to placing public engagement and meaningful dialogue with directly affected communities and other stakeholders at the heart of the development and delivery of our plans for improving the route.
"We want to ensure that communities have the opportunity to comment on the proposals for the scheme at every stage in the process.
“From today, we are launching a new website for the design work and the eleven corridor options under consideration can be viewed there.
“Please visit the site and give us your input by 30 October.
“We recognise the timescales for a an alternative to the current route are frustrating for the local community but in recognition of the pressures the current situation brings, we remain committed to progressing substantial shorter term investment in the existing A83 in tandem with the work to identify a permanent solution as part of a two phased approach.
Jo Blewett, Transport Scotland’s project director for the Access to Argyll and Bute (A83) project, said: “This is the first of several engagement exercises that will take place between now and Spring 2021 and at this stage we are particularly interested in any local constraints or issues that will help inform our design and assessment work.
“As part of our design work, we are also seeking contact from local community groups to help plan our future programme of engagement.”
Transport Scotland said £13.6 million had been spent so far on landslide measures at the Rest and Be Thankful and the Old Military Road below it, which is designed to be an emergency diversion route during its closure.
However, landslips have closed that road too.
The work has included four roadside “catch pits” which can hold a total of almost 15,000 tonnes of debris.
Work is scheduled to start on another catch pit next month, with more being considered.
The IAM RoadSmart motoring group said knowing the cost and environmental impact of the options were vital.
‘Verging on the useless’
Neil Greig, its Scotland-based policy and research director, said: “Such a varied selection of options will be welcomed by the people who are most directly affected by the problems of the A83 at the Rest and Be Thankful.
"Whilst we appreciate this is the first step in the process, asking people to choose routes without any financial or environmental information is verging on the useless.
"It is virtually impossible to compare local improvements with new bridges or new roads cutting a swathe through the pristine Argyll countryside.
"A long-term solution is vital so consultation is a good idea but ultimately it must not delay progress.
"IAM RoadSmart would encourage every user of the A83 to make their view known to Transport Scotland so they can get on with planning and construction.”