In the past few weeks, China has witnessed a population exodus unprecedented since the famine year of 1962, the apparent result of economic dissatisfaction and reduced border patrols because of the war against Vietnam.

Authorities in Hong Kong, the destination of almost all Chinese leaving the country, say at least 56,000 people have crossed the border legally or illegally since the beginning of the year, compared to about 100,000 for all of 1978.

Peking, whose relaxed travel rules have helped stimulate the exodus, has apparently done little so far to stem the flow. The Chinese press in recent months has acknowledged frankly the country's problems of overpopulation and underemployment. The rising tide of city youths swimming or crossing border fences into Hong Kong may ease somewhat urban discontent over lack of jobs and other services that have led to demonstrations lately in several Chinese cities.

Travelers report that Chinese coming into increasing contact with relatively wealthy foreigners and seeing more reports on Western life in the official press are outspokenly critical of their own living standard, although they often express hope that the new government will improve the situation. But Chinese who now have a chance to leave legally because of relatives abroad "all say they want to get out as quickly as possible," said one recent traveler who visited several such families.

The Chinese emigrants have deluged the U.S. immigration office here with 3,000 certified visa applications in February alone, compared to a rate of only about 30 a month a year ago. The brunt of the influx, however, is being absorbed by Hong Kong's overloaded housing and welfare services. Hong Kong officials now anticipate at least 300,000 new residents in this city of 4.5 million this year if the outflow from China continues.

"It's bloody frightening," said one Hong Kong officials. So far, several appeals by the British government to Peking have had no apparent effect. Hong Kong Governor Sir Murray MacLehose is expected to raise the matter when he visits Peking later this month, the first official visit by a Hong Kong governor to China since the Communist takeover in 1949.

Officials say a particularly significant jump in the number of illegal emigrants since the beginning of the year appears to be due in part to China's invasion of Vietnam. They suggest that the war has drawn away some Chinese troops previously used to partol the portions of Guangdong (Kwangtun) Provice near Hong Kong.

"Before people might be sneaking over in groups of five or six, but now they can come in groups of 30 or 40," one observer said.

According to a Hong Kong spokesman, 27,598 people with legal exit permits crossed the border this year through Sunday. In that same period, Hong Kong border police captured 7,061 Chinese attempting to cross the border illegally and turned them over to Chinese border guards. The government estimates that at least four illegal emigrants cross the border undetected for every one that is caught, making a total of at least 28,000 successful illegal emigrants so far this year.

At this rate, the number of people sneaking out of China this year will exceed the estimated total for all last year, about 32,000, by no later than the end of this month.

In 1978, about 71,000 people with legal exit permits crossed the border, while 8,192 illegal emigrants were caught and turned back to Chinese border officials. Peking has punished unsuccessful escapees lightly, cutting their grain rations slightly and detaining them briefly.

Any escapee who manages to elude the Chiness and Hong Kong border guards and reach the urban area of this British colony is allowed to stay. Several illegal immigrants interviewed here said they made many escape attempts before succeeding.

According to Hong Kong records, since the Communists came to power the China, the only time the flood of emigrants exceeded this year's occurred in May 1962, when about 50,000 Chinese crossed the border illegally in 23 days. The Great Leap Forward experiments of the late 1950s had lapsed in economic ruin, and bad weather had runied crops, creating a famine.

"They were just walking over the fences in droves," said one Briton who witnessed the 1962 influx, which reached a peak on May 23, 1962. On that day, 5,000 people crossed the border.

The 1962 deluge forced the British authorities for a while to arrest the illegal emigrants and turn them back to China, something they had not done up to then. Hong Kong had to revive this "repatriation" policy again in 1974, after some 24,000 illegal emigrants joined what was then a record 55,000 legal emigrants crossing the border.

Diplomatic discussions were held then in London and Peking and the number of Chinese entering Hong Kong with exit permits dropped to about 50 a day for awhile. The numbers then crept higher and mushroomed to a rate of about 200 a day last year. The increase in legal emigration grows out of the new, post-Mao government's desire to win favor among overseas Chinese, who provide a lucrative source of investment in the Chinese economy and an important source of political support in regaining control of Taiwan.

Local Chinese authorities appear to have been given permission to issue exit permits to Chinese residents whose overseas relatives have asked for them without any approval from higher authorities, bringing a flood of people into Hong Kong.

Many overseas Chinese seeking to bring families out of China live in Hong Kong. Those who live in other parts of the word, except for the United States and Candad, have found it difficult to persuade their home countries' immigration authorities to accept their relatives, and so many have remained here.

The illegal emigrants reaching here are in many cases young, single men, who help fill Hong Kong's factories with cheap labor.Many are highschool graduates sent to rural jobs in China because of a lack of office positions and college places. After training themselves in public swimming pools or commune reservoirs, some of them swam across Deep Bay or Mirs Bay to reach Hong Kong.

Authorities here say they do not known when the exodus will begin to diminish. They estimate that 200,000 ethnic Chinese refugees from Vietnam are now crowded into state farms and relcation camps in southern China. "A lot of them want to get to Hong Kong or the States, and have refused assignment to state farms," one immigration official said.

So far there is little evidence that they have joined the flow of illegal or legal emigrants from China, although Hong Kong is presently holding about 7,000 ethnic Chinese who arrived here by boat but appeared to have spent some time in China while en route from Vietnam.