The U.S. economy will continue to expand through 1979, though at a somewhat slower rate, and will not be derailed by rising inflation and climbing interest rates, according to the official forecast presented to the Business Council which is holding its spring meeting here.

"None of the consultants is forecasting a recession next year," Irving S. Shapiro told the opening session. Shapiro is chairman of E. I. dupont de Nemours & Co. and vice chairman of the Business Council, whose members include the heads of many of America's largest corporations.

The Du Pont chief also told the group that the business economists who prepared the forecast "have a 'show me' state of mind about President Carter's anti-inflation policy."

The businessmen were told that inflation in 1978 and 1979 will continue to accelerate, rather than decelerate, as the Carter administration would like. But the rise will not be drastic, with inflation staying below 7 percent. And unemployment will continue to inch down, according to the outlook prepared for the blue chip executives.

Treasury Secretary W. Michael Blumenthal, in an appearance, acknowledged "the inflation situation has worsened a little in recent months." But he held out some hope that the rate of price increases would abate in the second half of 1978, as they did in the second part of last year.

Despite the winter-related slowdown in real growth in the first quarter of this year, production has bounced back. As a result, this country's gross national product should still increase about 4.2 percent in constant dollar terms in 1978, the Business Council forecast predicted. Another 3.6 percent expansion was projected for 1979.

The strongest sector of the economy both this year and next should be capital spending, according to the forecast. Investment in plant and equipment is projected to grow by 6 percent in real terms in 1978 and by 6.3 percent next year.

"There is ample evidence that the economy is rebounding strongly this quarter so that our consultants continue to expect reat GNP to rise in the average of 4 to 4.5 percent for the full year," Shapior said.

THe expected unemployment rate for all of 1978 has been reduced since the last forecast to 6.2 percent and is put at 6 percent for 1979.

The inflation forecast has meanwhile been raised to 6.4 percent this year and 6.6 percent next year.

"On the positive side," Shapiro said, "and inflation rate of 'only' 6.6 percent would be well below some of the more pessimistic forecasts. But on the negative side it does not represent progress in meeting President Carter's desire for a lower rate of inflation, and it certainly is not a rate that the nation can live with indefinitely."

The Treasury Secretary, in his speech, said, "It is not clear that the current upswing in the inflation rate has run its course." But he added that "some relief is likely to be felt later in the year."

"Last year, consumer prices also rose more rapidly in the first half of the year, at about an 8.5 percent annual rate before falling back to less than five percent in the second half," he continued. "We hope history repeats itself. But we cannot afford to depend upon it."

Blumenthal then made a pitch to president's voluntary program to decelerate he rate of wage and price increases.

Some of the key Business Council members, in a session with reporters, declined to sign on for a commitment to numerically reduce the rate of price increases, as the president has sought, but said they would show restraint by justifying the cost basis for any price increase on a case-by-case basis.

Reginald Jones, chairman of General Electric Co., said that businessmen would be willing to respond to government jawboning, but would in turn jawbone the government, seeking some trade-offs on the inflation front.

The need for the federal government to show its earnestness in fighting inflation was a repeated theme.

"The test of whether jawboning works is whether the federal government can control its deficit" said Shapiro. "The rest will fall into place."

On the question of monetary policy there was widespread support for recent tightening moves by the Federal Reserve Board under its new Chairman G. William Miller.

But former Sears Roebuck Chairman Arthur Wood Roebuck Chairman Arthur Wood worried about he effect of higher interest rates on the housing and retail sectors, and recalled that "the last time the prime rate went to 10 percent plus was a serious jolt to the economy."