In early results of the US poll, Republican Donald Trump has won the electoral votes in conservative Indiana, Kentucky and West Virginia as predicted.
Democrat Hillary Clinton trails having captured only liberal Vermont.
The victories for both candidates in the four states were long predicted and not especially significant in a national race where opinion polls show Clinton has an edge.
Polls also closed in the vital battleground states of Virginia, Georgia, Ohio and North Carolina, although there were limited early results.
The North Carolina state elections board extended voting hours in eight Durham County locations after technical errors led to long waits.
South Carolina, Georgia and Virginia remained too close to call.
During the polls on Tuesday, there were long lines at many polling places.
The U.S. president is elected by Electoral College made up of 538 electors as against popular vote and to be elected president, a candidate must win 50 per cent plus one (51 per cent) electoral vote.
The states that are “solid” Republican are Alabama, Alaska, Arkansas, Idaho, Indiana, Kansas, Kentucky, Louisiana, Mississippi, Missouri and Montana, Nebraska, North Dakota, Oklahoma, South Carolina and South Dakota.
The others are Tennessee, Texas, West Virginia and Wyoming with a total of 157 Electoral College votes while the “lean” Republican states are Georgia, Iowa, Maine, Second Congressional District, Ohio and Utah totalling 47 electoral College votes.
On the other hand, the “solid” Democratic states are California, Connecticut, Delaware, District of Columbia, Hawaii, Illinois, Maine, Maryland, Massachusetts, New Jersey, New York, Oregon, Rhode Island, Vermont, Washington, Minnesota and New Mexico totalling 200 Electoral College votes.
The “lean” Democratic states are Colorado, Michigan, Pennsylvania, Virginia and Wisconsin with a total of 68 Electoral College votes.
The battleground states, which have 66 Electoral College votes up for grabs are Arizona, Florida, Nevada, Nebraska Second Congressional District, New Hampshire and North Carolina.
Each of the 50 states, as well as the District of Columbia, has a certain amount of Electoral College votes to award a candidate, based on the number of members of Congress it has.
This is roughly in line with each area’s population and the votes are given on a winner-takes-all basis, except in Maine and Nebraska.
In 2008, President Barack Obama won 53 per cent of the vote but this led to 68 per cent of the Electoral College vote.
Clinton led Trump, 44 percent to 39 percent, in the last Reuters/Ipsos national tracking poll before Election Day. A Reuters/Ipsos States of the Nation poll gave her a 90 percent chance of defeating Trump and becoming the first woman elected U.S. president.
In a campaign that focused more on the character of the candidates than on policy, Clinton, 69, a former U.S. secretary of state, and Trump, 70, a New York businessman, accused each other of being fundamentally unfit to lead the country.
Trump again raised the possibility on Tuesday of not accepting the election’s outcome, saying he had seen reports of voting irregularities. He gave few details and Reuters could not immediately verify the existence of such problems.
Financial markets, betting exchanges and online trading platforms largely predicted a Clinton win, although Trump’s team said he could pull off a surprise victory like the June “Brexit” vote to pull Britain out of the European Union.