With the flush of political triumph accompanying today's signing of the peace treaty, Prime Minister Menachem Begin's Likud Party has begun to make capital out of peace with Egypt.

Some party strategists have been talking again -- as they did following the original Camp David peace agreement -- about calling for new elections to expand Begin's base in the parliament.

The Likud, in splashy advertisements in today's newspapers, declared triumphantly that its toughest 1977 campaign promise had been fulfilled.

"Only 20 months after the elections... and what had seemed only a dream has become a reality -- the unbelievable has happened. Thus we have fulfilled our promise," the Likud boasted in one advertisement.

During the campaign, the Likud had been attacked as the "war party" by the Labor alignment, and Begin's hard-line stance against concessions to the Arabs was a central issue.

Some strategists in the Likud blochave been talking about forcing new elections to ride the wave of peace success to a larger majority in parliament and to tack two more years onto the party's mandate.

Other party officials, however, argue that it could take five months to arrange new elections, and that it is impossible to tell what the political climate in Israel will be like then because of the country's economic problems and the prospect of disputes over the autonomy negotiations for Gaza and the West Bank.

To hold new elections, Begin would have to resign and the Knesset, by at least a 61-vote majority, would have to dissolve itself. Israeli President Yitzhak Novon would then appoint Begin to head a caretaker government, and the political factions would start putting together lists of candidates for the parliament.

Whether new elections are held may depend on how many Likud hawks in the Knesset follow through with their threats to resign over the peace treaty. So far, the only one certain to leave is Moshe Shamir of the rightist Laam faction, who has urged the other Laam members to follow suit.

Although she has threatened to quit Begin's Herut Party, part of the Likud bloc, Geula Cohen has not yet made her move and some party officials are trying to persuade her to stay. Yigael Hervitz, a former Cabinet minister who voted against the treaty in the Knesset, has not decided whether to leave.

Party strategists say that if four or more Knesset members quit the Likud now or after the Herut Party convention in June, there may be no avoiding early elections because Begin will encounter difficulty maintaining a Knesset coalition during anticipated fights over Israel's soaring inflation and other domestic problems.