Somerset County Council is proposing stopping funding 20 of the county's libraries.
The move would leave 14 libraries paid for by the council. The remainder would have to be taken over by the community to stay open.
Those which would no longer get cash from the council include Cheddar, Glastonbury, Ilminster, Martock, Shepton Mallet and Somerton.
The proposals are outlined in a document on the council's website.
In the paper the council says it needs to save about £75m over the next three years and this is a "very difficult challenge".
It says all areas of council services are being looked at and the new look service would mean a 25% saving on the current library service budget of £5.4m.
Under the proposals, which will be considered by the council's cabinet in February, Somerset County Council would continue to support 14 of the most used libraries.
Of these 10 would have self service equipment installed to cut running costs.
The number of mobile libraries would be reduced from six to two, with the remaining two used to help cover areas where a static library is no longer funded or a high community need has been identified.
A series of drop-in sessions are planned for the new year for the public to have their say on the proposals.