Japanese car companies, computer makers and other manufacturers are beginning to feel the pinch of the yen's strength against the dollar.

Starting tomorrow, Toyota Motor Sales U.S.A. Inc., following the lead of a number of other Japanese car manufacturers, will increase the prices of its cars and trucks an average 3 percent, or $269, to counter the rise of the yen.

In the past two months, Mitsubishi Motor Sales of America, American Honda Motor Co., Nissan Motor Corp. and Mazda Motor Manufacturing U.S.A. Corp. raised prices on their 1986 vehicles to keep profit margins up.

The dollar has been on a downtrend since last February, when it hit a high of 255, finishing 1985 at Tuesday's close of 200 yen, compared with 251.85 on the last day of 1984.

The change in the dollar-yen relationship hurts profits for American subsidiaries of the Japanese companies because they sell their merchandise for dollars but purchase them for yen in Japan. They either buy yen with their dollars or pay in dollars, which the Japanese parent company then converts to yen. In either case, the dollars are worth fewer yen.

Many economists had predicted that foreign firms would not raise their prices so soon in efforts to keep their U.S. market share. But in addition to the yen-dollar problem, Japanese car companies are facing stiffer competition from American auto makers who are beefing up their own sales through discount financing programs, economists said.

The high value of the dollar over the past two years has been blamed for the increase in the trade deficit, the loss of more than 200,000 jobs in manufacturing and some of the troubles plaguing American farmers, who until recently had been big exporters.

The dollar started falling after reaching a peak last February. In September, its slide was enhanced by an agreement between the United States and four of its allies to attempt to push the dollar down further.

Since February, the dollar's value has fallen 21 percent, with half that decline occurring since the September agreement. Many economists said however, that it would take an even steeper drop to have a noticeable effect on the U.S. merchandise trade deficit, which ballooned to $13.7 billion in November from $11.5 billion in October. The nation's trade deficit with Japan also grew, from $3.2 billion in October to $4.6 billion in November.

Government and private economists also have noted dollar-related price increases of important industrial machinery from Japan and West Germany, computer parts from Europe and other manufactured goods. The Labor Department's index of import prices, excluding fuels, increased in the third quarter for the second consecutive quarter after declining for more than a year. The rise in the index has coincided with the dollar's decline since February.

Economists said it is too early for the increased prices to make much of a dent in the record U.S. trade deficit. The trade deficit next year probably will be higher than the expected record $140 billion to $150 billion shortfall for 1985, according to Beryl Sprinkel, chairman of the Council of Economic Advisers. But by the end of 1986, he said, the deficit picture should begin to improve.

Data Resources Inc. said in a recent report that the merchandise trade deficit is expected to narrow from $143.8 billion in the third quarter of 1986 to $134.4 billion by year's end. By 1987, the deficit should fall to $121.8 billion, DRI said. "Continued devaluation of the dollar will stimulate exports while preventing further import penetration," the DRI study said.

One phenomenon being observed by economists is that as the value of the dollar declines, and before the higher prices of imports can reduce their volume, the value of imports into the United States rises, worsening the trade deficit. Then, as price increases begin to trim the volume of imports, the trade deficit should improve.

There is a lag in the effects that the weakening dollar exchange rate has on prices, and some importers try to prevent price increases and their resultant lost market share by absorbing lower profit margins for a time, economists said.

"The resultant squeeze on importers has only begun to trigger price increases," Townsend-Greenspan & Co. Inc. said in a recent report. "It would appear, therefore, that further declines in the exchange rate will be required before prices for imported goods rise sufficiently to curtail the demand for imports" and reduce the trade deficit.