One of Mexico's saucier cartoonists not long ago drew a large, full-uddered beast called "penex," which also is the name of the national oil company. "Nourishment for politicians and businessmen," said the caption below the mammary gland.

It may be the most cynical view to take, but it captures the way many Mexicans talk about their oil wealth, little of which they feel has come their way so far.

Glowing media reports tell them that the 7 1/2-percent growth rate their country had last year was the continent's highest, that companies reported record profits and that Mexico is sought after abroad as never before.

Yet most people's problems have been aggravated by oil-fueled inflation -- 30 percent last year -- which has eaten away their real salaries. Even for Mexico's leadership, the look of pride at joining the oil powers is turning into a frown.

The impressive oil wealth, officials admit, has served so far to worsen the distortions in a society in which a small number of persons control much of the wealth while 75 percent of the population earns less than the legal minimum wage.

When Mexico first decided to exploit its largely untapped oil and gas, technocrats were dispatched to study the methods of other nations that were using oil revenues to end their underdevelopment. As a semi-industrialized nation, Mexico concluded it would draw on all available models simultaneously. Its short-term strategy was to boost investment and spur growth in industry, while in the medium-term it could cut back unemployment, boost consumption and cater to the basic needs of a neglected majority. Congestion and inflation, the chronic ills of other oil nations, should be avoided at all costs, officials decided.

But the past year has shown that even with its eyes open, Mexico has not been able to avoid all the classic pitfalls that come with oil discoveries. nRailways, roads and ports, designed for a slower era, have become clogged with goods. Ambitious projects are out of scale with available human resources.

The oil syndrome of exporting energy and importing almost everything else appears to be a trend. In 1980, oil and gas accounted for two-thirds of Mexico's export earnings. But while imports jumped 55 percent, exports of manufactured goods rose only 6 percent.

This year, planners foresee another 50-percent increase in imports. The import bill -- expected to reach $22 billion -- should be about as much as Pemex hopes to get for its oil and gas exports.

Mexico produced approximately 700,000 jobs last year, which barely kept pact with the number of new persons entering the job market. The projected number of jobs in the oil industry, close to 800,000, therefore will not substantially reduce Mexico's dramatic unemployment. Of a labor force of 20 million persons, 8 million do not have full-time jobs.

Another problem is that next year's anticipated growth rate of 8 percent is likely to keep inflation spiraling.

In the coming year, the government argues, more benefits also will reach the 40 percent of the population living in poor rural ares and the 15 percent in urban slums. The government has increased the nation's 1981 education budget by 44 percent and social welfare by 79 percent. Staple foods will continue to receive vast official subsidies to take the worst sting out of inflation.

In the meantime, Mexico retains its crucial escape valve, which is not likely to be shut off in the near future by the current administration of President Jose Lopez Portillo. The number of jobless crossing illegally into the United States has grown perceptibly during the past year because of severe drought in the north, according to U.S. officials.

As the economy booms, it is producing a side effect that Mexico's nationalistic politicians are very wary of but can do little about. Mexico's economic relations with the United States are expanding rather than shrinking. Mexico already carries on two-thrids of its trade with its northern neighbor and is becoming increasingly dependent on the United States for food.

In 1980, Mexico bought a record quantity of grains -- more than 10 million tons -- abroad, of which nearly 7 million tons came from the United States.

With bilateral trade more than doubling to $29 billion during the past two years, Mexico has become the United States' third largest trading partner. Despite the growing U.S. energy bill, the trade balance is still close to $1.5 billion in favor of the United States.

In the American business mind, there appears no lack of confidence in Mexico's oil-heated economy, despite all its problems. Projections for 1981 are that American investors will be pouring $1.2 billion worth of investment into Mexico.