Liberal Democrats and the Scottish Nationalists are vying for second place and the contest is also the first electoral test for David Cameron's new-image Tory party.
Labour insiders have admitted the expect the party's majority to be reduced to between 2000 and 3000.
The by-election was caused by the death of long-serving Labour MP Rachel Squire.
Meanwhile, campaigners fighting to remove tolls from the Forth Road Bridge have staged a demonstration on the crossing.
The protesters marched across the bridge carrying banners yesterday, and tried to lay a wreath at the offices of the Forth Estuary Transport Authority.
The marchers were accompanied by Tom Minogue, a veteran anti-toll campaigner and independent candidate in today's by-election.