The Senate is taking final action on plans to phase out tariffs between the United States and Canada and end a variety of other trade barriers.

"I consider this the most significant economic agreement the United States has ever entered into with another country," said Sen. Bob Packwood, R-Ore., a leading supporter.All tariffs between the two countries would be phased out over 10 years under the agreement, which was signed Jan. 2 by President Reagan and Canadian Prime Minister Brian Mulroney. Some other barriers also would be ended.

The bill to start the phase-out won strong House approval Aug. 9 and the same is expected in the Senate in a vote set for Monday. The measure then goes to Reagan's desk. But that does not mean the agreement will go into effect anytime soon.

The bill would authorize Reagan to put the agreement in effect starting Jan. 1. How soon the ball gets rolling, however, actually depends on when the Canadians can get their counterpart legislation through Parliament.

Canadian legislation has won approval from the House of Commons in Ottawa but will die in the Senate if, as expected, Mulroney calls parliamentary elections within the next two or three weeks. The Canadian legislative process would have to start from scratch..

A free-trade agreement ends tariffs on shipments between the countries involved.

Israel is the only other country with which the United States has a free-trade agreement. But the volume of trade with Israel is minor compared with the flow of goods in both directions across the northern border.

In 1987 alone, $131 billion in merchandise flowed over the U.S.-Canadian border, marking Canada as the No. 1 trading partner of the United States.

When services are added to the calculation, total trade between the two countries amounted to $166 billion. Japan was No. 2 with $116 billion in merchandise trade with the United States last year.

On another front, a showdown is expected Tuesday on a proposed $1.20 an hour increase in the minimum wage over three years.

The minimum wage has been frozen at $3.35 an hour since 1981 and inflation has reduced its purchasing power to about $2.60.

The bill sponsored by Sen. Edward Kennedy, D-Mass., would raise it 40 cents an hour in each of the next three years, providing direct benefit to about 15 million workers.

"The working people of this country have been waiting eight years for a cost of living increase," Kennedy said.

Reagan and Vice President George Bush have softened their opposition but only on condition that any increase is coupled with a subminimum training wage.

Neither Reagan nor Bush has specified how much of an increase he favors. Bush's running mate, Sen. Dan Quayle, R-Ind., in June proposed an increase to $4 an hour over two years.

An amendment introduced on the Senate floor last week by Sen. Orrin Hatch, R-Utah, would allow employers to pay 80 percent of the minimum to newly hired workers for the first 90 days they are on the payroll.

The key vote will be on a substitute amendment by Kennedy to Hatch's proposal. Kennedy's plan would slightly expand coverage of an 85 percent subminimum wage - currently $2.85 an hour - for full-time students that is now in the law. About 100,000 students are paid that subminimum.