Chrysler Corp. yesterday reported third-quarter net income of $316.2 million, a 20.9 percent increase over the $261.6 million the company earned in the same period last year.

Earnings declined at American Motors Corp., the smallest of the four U.S.-based auto makers, which has been hurt by a shortage of new products and by unfavorable market conditions affecting its main line of passenger cars.

AMC lost $19.1 million in the third quarter compared with a year-ago gain of $2.5 million in the same period; but AMC's third-quarter losses were the smallest so far in what is turning out to be a dismal fiscal year for the company.

AMC lost $29 million in the first quarter and $70.4 million in the second period of 1985. The company's year-to-date losses amount to $118.5 million. AMC reported no per-share earnings in the third quarter of 1984.

Chrysler's latest quarterly profits work out to $2.75 per common share compared with $1.88 in the third quarter of 1984.

But Chrysler's fourth quarter will include the effects of a 12-day strike against the company's plants in the United States and Canada.

Domestic auto industry analysts predict that the walkout by the United Auto Workers union, which officially ended yesterday, will reduce Chrysler's fourth-quarter-1985 results by at least $100 million. One Detroit-based analyst believes the cost could be as high as $250 million when all of the strike accounting is done.

In all, the nation's three largest auto makers earned $1.14 billion during the third quarter, an 8.6 percent improvement over their $1.05 billion combined earnings during the same period last year.

But the latter part of the 1985 third quarter was marked by aggressive, cut-rate auto financing programs. All Big Three car companies -- General Motors Corp., Ford Motor Co. and Chrysler -- said that the below-8-percent finance campaigns hurt their profits. GM and Ford both reported a drop in operating income for the quarter.

AMC also had a below-8-percent finance program. But, in terms of product, the company had little to offer other than its Renault Alliance and Encore passenger cars, slow-selling subcompacts that already had been selling at prices below those of many other competitive models.

Ford earned $313 million ($1.70) for the period, 17.5 percent less than the $379.7 million ($2.05) it earned in the third quarter of 1984. Ford's operating profits for the period amounted to $155.2 million, less than half of the $362.7 million in operating profits made in last year's third quarter.

GM reported a third-quarter net income of $516.5 million ($1.46), 23.9 percent higher than the $416.8 million ($1.31) earned in the year-ago quarter. But GM reported an operating loss -- money related to its auto manufacturing business -- of $20.9 million for the period.

Chrysler, which has enjoyed lower production costs than its two largest competitors, managed to make both net income and operating gains during the third period. The company reported record third-quarter operating earnings of $451.8 million, a 72.5 percent increase over operating profits of $261.9 million during the same period in 1984.

Chrysler yesterday also announced cut-rate financing or a $500 cash-back allowance on two sports sedan models. For loans up to 48 months long, Chrysler is offering 8.6 percent financing on its Chrysler Lebaron GTS or Dodge Lancer models.