When Annelise Kappler lugged her husband, convicted Nazi war criminal Herbert Kappler, out of a military hospital here in an oversize valise on wheels a week ago, she dramatically underlined a growing problem - the leakiness of Italian jails.

"This is the ultimate proof that in Italy breaking out of jail has become as easy as checking out of a hotel," said a disgruntled Italian policeman.

So far this year, more than 200 convicts have escaped from prison in this country, most in jailbreaks involving such time-honored methods as sawing off bars or climing down sheets.

The same day Kappler escaped to West Germany, eight convicts broke out of a jail in Bergamo. Since then, at least five other escapes have been reported, and police sources say that if the jailbreaks continue at this rate this year's total could top last year's 424 escaped convicts - well more than one day.

Severe overcrowding and a scarcity of prison guards - 11,000 who work seven-hour shifts to guard a prison population of 35,000 - are thought to be the major causes.

The present government, like its predecessors, has promised to pass a long-delayed prison reform bill that would improve living conditions, increase rehabilitation programs and established firm distinctions in treatment between convicted criminals and some 18,000 as-yet-untried persons left languishing in jail by the creaky mechanisms of the Italian courts.

For now, however, the only immediately practical plan under consideration to alleviate the situation is a general amnesty for minor crimes that was recently proposed by Christian Democratic leaders.

Critics of the proposed amnesty which would be the 41st since 1944, say it would do little to improve the system's basic ills. But with Italy's major penitentiaries bursting at the seams an amnesty could reduce the prison population drastically, if only temporarily.

Regina Coeli prison in Rome has room for 700 inmates, but houses 1,150: Naples' prison at Poggioreale holds, 1,700 prisoners, although it was built for 1,200.

The last amnesty, in May 1970, provided clemency to 15,000 persons. A new law that would provide amnesty for persons guilty of minor offenses for persons guilty of minor offenses could benefit close to 10,000 prisoners.

"An amnesty would give the government a breathing space in which it would make substantial progress on other measures, such as the construction of new jails including eight maximum-security prisons, and higher pay and better training for oveworked guards," said a Justice Ministry official.

"But whatever it is, something has got to be done if our government is to be able to show that even if it can't prevent crime, it can force convicted criminals or persons awaiting trial behind bars to stay put."

The Kappler escape has heightened the need for improved prison security if government credibility is to be maintained. But the uproar over the former SS colonel's escape to West Germany goes beyond the technical aspects of a well-planned prison escape that could have been prevented.

Kappler, 70 and reportedly suffering from terminal cancer, had been transfered to the military hospital from a prison on Gaeta, in southern Italy. He is now in West Germany.

Kappler's escape has caused consternation and embarrassment here.Two carabinieri , or national police men were arrested and four earabiniers officers were transferred following the incident. A meeting between Italian Premier Giulio Andreotti and West German Chancellor Helmut Schmidt was postponed.

Many Italians appear to feel that the country has been made to look foolish. Major Italian newspapers have referred to the escape as a "national humiliation." Calls have been made for the resignation of the minister of defense, who is responsible both for military hospitals and for prisoners of war.

There has been widespread speculation that leftist terrorists, rightist extremists, the Italian secret service or the German Red Cross were behind what others think was simply a well-though-out plan by a woman determined to bring her suffering husband back home to die.

The fact is that Kappler had become a major symbol of recent Italian history.

Convicted in 1948 of conducting the reprisal slayings at the Ardeatin caves in Rome of 335 Italians, 70 of whom were Jewish, after partisans had killed 32 German soldiers in an ambush. Kappler's life imprisonment has been considered a victory over Fascism by most of Italy's political parties.

In November, an order for his release in response to pleas by Kappler, his wife and Bonn officials provoked mass protests by relatives of the Ardeatine victims and most of Italy's major parties. The release order was later reversed by a high military court on the ground that Kappler was a war criminal and thus not subject to regulations covering ordinary convicts.

The fact that Kappler escaped so easily has left many Italians bitter and confused.