Not long after Zimbabwe gained independence in 1980, Mary Murumbwa packed her humble belongings and headed for ''greener pastures.'' Better land had been promised by the black liberation forces during their struggle to topple the white rulers of Rhodesia. Now that those forces were in power, Mrs. Murumbwa simply took what had been promised - a small patch of land here on the banks of the Chinyika River where she could eke out a subsistence living.
Tens of thousands of peasants are doing the same thing in this country - and setting off a rural squatting phenomenon that government officials concede ''is out of control.''
The trend raises a fundamental question about this country that has been independent and black-ruled for three years: Can Prime Minister Robert Mugabe satisfy the land grievances of the huge black peasant population?
Further, can the lot of black peasants be improved without upsetting the almost exclusively white commercial farm sector, which is so successful as to feed the country and still provide for exports?
Satisfying the land demands of the peasants may sound like something a politician might forget once in office. But in Zimbabwe the peasant population provided the revolutionary groundswell that made the ''war of liberation'' uncontainable for the previous white government.
Dr. E. M. Chiviya, an assistant secretary for lands, resettlement, and rural development, says: ''The basic grievance that led to independence was the rural black population's dissatisfaction over land issues.''
The way Dr. Chiviya sees it, Prime Minister Robert Mugabe's chances of being reelected in 1985, when the next election falls, will hinge directly on the land issue.
The government has an ambitious land resettlement policy that, at least in theory, would allocate more and better land to blacks without damaging the white commercial farm sector. The government wants to resettle 162,000 black families over the next three years on land that the government will buy from white farmers on a ''willing buyer, willing seller'' basis.
However, there are a number of sticking points in this plan. First, the objective of settling 162,000 families seems unattainable, given the slow pace of the program so far. Since independence in 1980, fewer than 15,000 families have been resettled. The administrative difficulties of starting such a huge program are considerable.
Another growing constraint is money. The government claims the program is slowing because of inadequate funds to buy land. With Zimbabwe sinking into recession and demands growing, it is difficult to see the financial constraints lessening in the foreseeable future.
Further, the resettlement objectives increasingly appear at odds with the needs of the white commercial farm sector. Zimbabwe's commercial farmers union calculated that about 10 million acres of land are available for government purchase. But a rough estimate of the amount of land needed to settle the number of black families the government has targeted comes to 22-to-24 million acres. Will this land be forcibly pried from the hands of white farmers, to the detriment of the commercial farm sector?
The basic grievance over land in Zimbabwe stems from the allocation of land by the former white rulers. Rural blacks were granted about 40 million acres - on which about 4 million blacks now live. Whites received only slightly less land - about 34.6 million acres - but the land was of higher quality and it was far less populated. There are about 4,700 white commercial farmers today.
In broken English, Mrs. Murambwa describes the conditions in the black rural areas as ''not enough land, too crowded.'' Those conditions led her to move to Chinyika.
The Chinyika land resettlement project, about 90 miles east of Harare, is typical in that it uses land bought from white farmers and land vacated by white farmers in wartime. It is also typical in having a huge squatter problem.
Lovemore Tsotso, the resettlement officer here, has some 2,500 families illegally squatting on the land, compared to 1,570 families who have been officially resettled.
The government has set up a task force from military and other departments to get tough with squatters. But given the political sensitivity of the issue, persuasion is being used rather than force. Here at Chinyika the trend is simply to accept squatters who would qualify for resettlement and work them in to the project.
The aim of resettlement is to make the black families self-sufficient with enough surplus crop to earn some cash each year. Even such modest goals are jeopardized in 1983, as Zimbabwe experiences one of its worst droughts.
The Chinyika project was launched in September. Its first crop already looks like a complete loss. The government is trucking in maize to feed people here.
Running his fingers over a withered stalk of corn, Mr. Tsotso says ruefully, ''We're not off to a good start.'' Other articles appeared Jan. 24 and 25. ZIMBABWE FACTS: Population:
10.5 million (est.) Work Force:
1.4 million in the ''modern economy''
.29 million agriculture
.17 million manufacturing and construction
.07 million mining
GNP: $5.79 billion (Dec. '81) of which agriculture is 18 percent and industry is 32 percent
Inflation rate: 16 percent ('82 est.)
Per capita income: $13,480 for whites, $314-$655 for blacks
Imports: $1.34 billion ('81), particularly manufactured goods and equipment, petroleum, transport equipment
Exports: $0.94 billion ('81) of tobacco, corn, minerals
Natural resources: Chrome, coal, asbestos, copper, nickel, gold, iron ore, vanadium
Source: US State Department