Domestic car sales took a startling 10 per cent plunge in mid-December, leaving auto companies puzzled by the drop in sales at the end of what had been a banner year.

For the Dec. 10-20 period, sales of domestic models were 201,143, compared with 223,556 for the same period a year earlier. There were eight selling days in each period.

All four car companies recorded losses. Ford Motor corp. was off 6.7 per cent, General Motors 8.5 per cent, Chrysler 17 per cent and American Motors 39 per cent.

For the calendar year through Dec. 20, the industry still held a 6.5 per cent gain over the comparable 1976 period. But that was attained on the strength of a strong finish for the 1977 models and the normal spurt of sales at the start of the new model year for 1978 cars.

Company executives tried to minimize the trend that has lasted since mid-November, citing the overall gain this year and noting that the current figures were being compared to a phenomenal period a year earlier.

When pressed for an explanation of the downturn, most companies said they were at a loss for a reason.

"All of a sudden things just turned down," an AMC spokesman said. "Nobody can pin it down. It could be the holidays. But who knows?"

A Ford spokesman said the company was not contemplating any reaction to the sales trend, such as reduced production.

"We consider it a blip in the pattern," he said. "But if the industry stays at this level through January, then there's going to have to be some looking around.

"Everything you look at is up, such as business indicators and consumer confidence. There's nothing in the hard data to explain why car sales should taper off. They should at worst be even."

GM, the industry leader, said the slump was too short to indicate a pattern. But as recently as Dec. 2, GM chairman Thomas Murphy was predicting his company's sales, including imports, would hit 5.2 million.The mid-December results indicate, however, that that projection will fall about 50,000 short.

Analysts noted sales a year ago, the second - highest on record, were "exceptionally strong," and characterized this year's figures as not really that bad.

"Since the model year began in October, sales of all GM vehicles are running ahead of the 1977 model year," said Robert D. Burger, vice president of marketing at GM.

But industry analysts noted GM continues to have trouble with its intermediate models.

"GM is not getting the sparkle out of its new models, the sparkle you've got to get," one analyst remarked.

In contrast. Fords new models, Fairmont and Zephyr, are selling well, he said. The Ford offerings are an inch shorter than some GM's new models, but cost less.Buyers may be responding to what they think is a bargain, said the analyst, who preferred his name to be used.

Ford's slump was blamed on dealer incentive contests which ended in the early December period, according to Bennett E. Bidwell. For car and truck vice president.

For the period, GM sold 118,980 cars compared with 130,095 a year ago. Ford sales of 55,660 were off from 59,701. Chrysler delivered 22,775 compared with 27,575. AMC sales were 3,728 versus 6,185 in the year-ago period.

For the calendar year through Dec. 20, sales were up 6.5 per cent to 8,857 - 906 or 29,724 per day from 8,349,200 or 27,917 per day. The daily rate is the industry selling yardstick for comparing periods.

Ford sales for the year gained 13.9 per cent from 2,183,799 to 2,480,084; GM's rose 7.8 per cent from 4,656,402 to 5,001,694; Chrysler was down 5.3 per cent from 1,266,239 to 1,195,593, and AMC was off 24.7 per cent from 240,760 to 180,535.