The latest surveys suggest Switzerland's main party, the populist right-wing anti-immigration Swiss People's Party (SVP), will make gains and possibly tip the scale in parliament towards a slight centre-right majority.
The expected shift comes as surging numbers of migrants and refugees moving through Europe have heightened the focus on the issue in Switzerland, even though the wealthy Alpine nation has yet to be significantly affected by the crisis.
About a quarter of Switzerland's eight million inhabitants are foreign nationals, and immigration and asylum policies tend to figure among voters' top concerns.
Only nine per cent chose the runner-up issue -- Switzerland's relationship with the European Union -- as the most important.
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Ties with the EU were badly hit by a narrow Swiss popular vote in February 2014, championed by the SVP, in favour of restricting immigration from the bloc.
SVP, the most visible party on both the top issues, hit 28 per cent support in the latest poll -- up from the 26.6 percent it managed in the 2011 election and close to the record high 28.9 per cent it won in 2007.
The centre-right Liberals, in third place, are also seen gaining ground from the 15.1 per cent they took in 2011, at the expense of the Christian Democrats, the Greens and other smaller parties in the house.
Polling stations will open at different times across the country and stay open for just a few hours, closing by noon (1000 GMT), as most Swiss vote in advance by post or online.
In all, 246 seats are up for grabs -- 200 in the lower chamber and the remainder in the upper chamber.
Switzerland's famous system of direct democracy allows citizens to voice their opinions on a large range of issues every few months, downplaying the importance of the parliamentary vote.