Egyptian President Hosni Mubarak, on his first trip to Washington since he was catapulted into power by the assassination of Anwar Sadat on Oct. 6, plans to ask the Reagan administration for a big increase in military assistance and far greater flexibility in its handling of the annual $1 billion in U.S. aid here.

Mubarak, who arrives Tuesday, has been preparing meticulously for his American debut for several weeks. He has already said publicly in general terms what is on his mind and what he is hoping to obtain during his visit.

In part, he is calling for a new, flexible U.S. approach to its huge economic assistance package in order to use up more of the $2.5 billion now unspent.

In part, too, he is seeking approval from President Reagan for a five-year defense plan under which Washington would provide $6.5 billion in loans and grants to allow Egypt to complete renovation of its previously Soviet-equipped armed forces, according to Egyptian military sources.

But the great unspoken concern here is the impression Mubarak will make on the American public as the successor to Sadat, whose fame and popularity in the United States were tremendous.

The stocky, 53-year-old former bomber pilot has a totally different personality and style of rule from Sadat's, and he has accentuated these differences by avoiding the quirks and flourishes that got his mentor into deep trouble at home.

Where Sadat was flamboyant, dramatic and rhetorical, Mubarak is simple, direct and terse. Where Sadat loved to retreat into lonely solitude and then announce surprise decisions all on his own, Mubarak has gone out of his way to consult a wide range of advisers, experts and even opposition leaders before taking any action.

The new Egyptian leader has begun setting his nation on a new course in foreign and domestic policy in hopes of resolving a broad range of problems he inherited from Sadat.

Chief among these is Egypt's isolation in the Arab world as a result of Camp David and the peace treaty with Israel, severely aggravated by Sadat's practice of hurling insults at every Arab leader who disagreed with him. Mubarak has already begun reopening doors to the Arab world as well as to the Soviet Union and the nonaligned bloc, from which Egypt was also excluded after the Camp David accords.

Mubarak has been stressing the word "nonalignment" in his description of Egypt's foreign policy and he made it clear to the Soviet Union, whose ambassador Sadat expelled in September, that he would like to improve relations.

At home, Mubarak has been extremely busy during his first four months in office trying to make peace with the many groups in Egyptian society--Christians, the political elite, professionals, leftist opposition groups and even the Moslem Brotherhood--alienated from the government during Sadat's last stormy years.

He has released 242 of the 1,536 persons Sadat detained during his sweeping crackdown on all forms of opposition to his rule in September. Among those freed were top officials of legal opposition parties, independent critics of Sadat, Coptic priests and bishops, leftists, including some communists, and several Moslem religious leaders, including the head of the Moslem Brotherhood, Sheik Omar Telmissani.

He has also restored scores of professors and journalists, dismissed from their jobs by Sadat, to their former posts.

The one group he has not spared, however, is the Moslem extremists. Not only has he not freed any of those leaders and members of extremist groups arrested by Sadat, but he has rounded up at least 2,000 more.

Mubarak plans to discuss his economic problems with Reagan and other U.S. officials and to ask for greater flexibility in the American aid program partly to help cure them. His main concern is understood to be the inability of Egypt to make full use of the $1 billion annual U.S. aid program.

The Egyptians feel there are too many restrictions on the use of U.S. funds, most of which are tied to specific development projects. They want authority to switch money from one project to another, depending on their own evaulation of which is going better, according to Agency for International Development officials here.

Part of the problem of the $2.5 billion in unspent U.S. aid stems from the commitment of money to projects that ran into trouble or never got off the ground, they said.

AID officials believe the problem can be reduced if Congress gives them authority to commit funds to a sector of the economy rather than to specific projects.