The Communications Workers of America early today began a nationwide strike by 155,000 members against American Telephone and Telegraph Co., disconnecting long-distance operators and shutting down most of AT&T's computer and telecommunications arms that serve thousands of business and government customers.

Shortly before the midnight contract deadline, CWA spokeswoman Rozanne Weissman said a settlement was unlikely "because the issues we are dealing with are quite complex . . . . Therefore, the CWA is going to be on strike at 12:01 a.m. There will be pickets at all sites around the country."

CWA President Morton Bahr and other officials remained in negotiations with AT&T officials late last night, trying to resolve disputes over wages, job security and changes in job classifications and pay levels.

"AT&T is disappointed in the union's action," said company spokesman Herbert Linnen. "We believe a settlement is possible . . . . AT&T has never wanted a strike. There is nothing to be gained by a strike."

The walkout is expected to idle 200,000 AT&T employes because 45,000 members of the International Brotherhood of Electrical Workers, whose contract also expired at midnight, are expected to stay off the job.

The strike will not disrupt local phone service, including directory assistance and telephone repairs, because local firms such as the Chesapeake & Potomac Telephone Cos. are no longer part of AT&T because of the 1984 breakup of the Bell System monopoly. Regional telecommunications firms bargain separately with CWA under contracts that expire Aug. 9.

The strike is expected to have little immediate impact on long-distance service because more than 90 percent of AT&T's 33 million daily calls require no operators.

But the walkout could substantially affect businesses and regional telephone companies that rely on AT&T to manufacture, install and repair their computers and telecommunications equipment, according to Wall Street analysts. Analysts said a strike also could affect the value of AT&T stock -- one of the most widely held stocks in America, with more than 2.9 million individual shareowners.

The AT&T strike idles 38,000 operators and thousands of clerical employes, skilled technicians and manufacturing workers. CWA last struck AT&T in August 1983 in a walkout lasting 22 days.

AT&T's 26 manufacturing plants in 18 states, closed for the weekend, are expected to remain shut during the strike. The walkout also may force the closing of many of the 700 Phone Center stores, Linnen said.

AT&T and CWA negotiators, during eight weeks of talks, made progress toward agreement on job-security guarantees and retraining programs sought by the unions. But the talks broke down primarily over wages and job-classification changes.

AT&T operators earn an average of $21,300 and skilled technicians earn $31,700. A major dispute involved AT&T's demand for several new job categories among its 20,000 systems technicians. AT&T contended that some of the "techs" did not deserve top pay because they performed less-skilled duties.

AT&T made a $2 billion profit in its last five quarters, prompting union demands for substantial pay raises. CWA criticized as "totally inadequate" AT&T's initial offer of a 5 percent raise over three years, contrasting it with larger raises for executives, including AT&T Chairman Charles L. Brown, who received a 33 percent raise to $1.32 million in 1985. AT&T yesterday raised its wage offer to 7 percent over three years.

But AT&T and Wall Street experts have said the company would not agree to larger raises because it has failed to reach profit targets.

AT&T has been seeking to restructure itself, reassign certain job duties and cut its labor costs as it enters into global competition in computers and telecommunications.

CWA and IBEW were seeking far-reaching guarantees to protect workers from layoffs, transfers and downgrading of jobs. More than 15,000 AT&T workers have been laid off since divestiture.