Alf Landon, the former Republican governor of Kansas who survived a landslide defeat in the 1936 presidential campaign to become a 20th century legend, died yesterday at his home in Topeka. He was 100.

In the more than 50 years since he carried only Maine and Vermont against Franklin D. Roosevelt, Landon showed a philosophic good humor and a rugged independence of outlook that made him an increasingly beloved and admired figure.

Continually keen-witted and physically active, Landon, a prosperous businessman, celebrated his 100th birthday on Sept. 9 and entertained President Reagan at his home three days before.

After complaining of internal pain late last month, he was hospitalized Sept. 28 at Stormont-Vail Regional Medical Center. He was treated for a gallstone and bronchitis before being released three days ago.

Landon, who served two terms as governor of Kansas, was the father of Sen. Nancy Landon Kassebaum (R-Kan.).

In a statement last night, the president said, "Alf Landon exemplified the very best in public service. He deeply loved his country, and he was motivated by a genuine desire to help his fellow man.

"As governor of his beloved Kansas, he brought a common sense wisdom to the statehouse," and as a presidential candidate he "spoke passionately and articulately on behalf of the principles on which our nation was founded," Reagan said.

"It was a special comfort to me to know he was just a phone call away," the president said.

Inevitably, Landon's 1936 loss, by 523 electoral votes to 8, a margin that has never been surpassed, made of him a symbol of overwhelming defeat.

But Landon had no illusions about his chances of winning against the Democratic incumbent Roosevelt, to whom millions looked as a symbol of the nation's determination to escape the clutches of the Great Depression.

The man whom contemporary journalists viewed as representative of the plain-spun virtues of his middle American roots -- friendly and simple, sound and sensible -- appeared to be unbroken by the nation's massive repudiation of his candidacy.

In a frequently played snippet of a radio interview, he could be heard observing dryly that the most remarkable aspect of his defeat was the "completeness of it."

Eventually he gave two grandchildren ponies named for the two states that he had won.

As the years passed, Landon's ability to place the defeat in perspective seemed to become as much a part of his image as the defeat itself.

That, combined with his zest for life, his casual amiability and his ability to offer trenchant commentary on world and national events, helped increasingly to make of him a widely admired elder statesman, the grand old man of the GOP.

Often, the opinions he readily offered reflected both the wisdom of experience and the independence that characterized his political career. Landon had been a member of the reform wing of his state's Republican party. He had campaigned against the Ku Klux Klan in the 1920s, and he had been among those who 75 years ago broke from the Republican Party to support the Bull Moose presidential campaign of Theodore Roosevelt.

Alfred Mossman Landon was born Sept. 9, 1887, in West Middlesex, Pa. His father, John Manuel Landon, was an oil prospector and promoter. His mother, Anne Mossman Landon, was the daughter of a Methodist clergyman. Landon was born in his grandfather's parsonage.

He attended Marietta Academy in Marietta, Ohio, and when he was 17, with oil fields opening in southeastern Kansas, his family moved to Independence, Kan.

In 1904, Landon entered the University of Kansas. After only one year there, he entered the law school. In the meantime, he showed a bent for campus politics, winning the nickname of "The Fox."

He received his degree in 1908 but showed little interest in pursuing the field in which he was trained, later describing himself in part as "a lawyer who never had a case."

He became a bookkeeper at a bank, invested part of his pay in oil drilling ventures, and, after three years, had banked $3,000. After borrowing more, he and three other men formed A.M. Landon & Co., a concern set up to develop what were known as strip oil wells.

Strip wells had lost much of their volume. Those who worked them tried to strip out as much as possible of what remained.

In 1912, the same year Mr. Landon set up his business, he and his politically active father objected to what they saw as the steamroller tactics by which the forces of President William Howard Taft dominated the Republican National Convention.

They bolted the party. Landon's father went as a delegate to the Bull Moose convention in Chicago that nominated Theodore Roosevelt, who was seeking to return to the White House after a four-year absence. Landon accompanied his father, and he returned to organize his county for Roosevelt.

The Bull Moose group later became the progressive faction of the Kansas Republican Party, with which Landon was linked.

He served for a time as secretary to the governor of Kansas and then in 1928 he became chairman of the state central committee. In 1931, he entered the gubernatorial primary.

He made what was described as a cracker-barrel campaign, entering crossroads stores in boots and an open shirt. The low-key campaign, in which he asked bystanders about their problems, but not for their votes, worked. In the bitter Depression year of 1932, the Democrats swept the nation, and Landon was the only Republican governor elected west of the Mississippi River.

In 1915, while Landon's star was rising in the oil business, he married Margaret Fleming. She died of meningitis three years later. Inconsolable, Landon left their infant daughter in the care of the child's grandparents and enlisted in the Army.

World War I ended while Landon, a first lieutenant, was still in training, and he returned to the oil business.

In 1930, he married Theo Cobb, and they had two children, John Cobb, and Nancy, who was elected to the Senate in 1978.

He described her victory that year, when he was 91, as "the thrill of a lifetime."

Reelected in 1934, as the only Republican governor to win that year, he compiled a record that blended traditional heartland conservatism with actions and stands seen as "progressive," including cutting his pay and introducing a graduated state income tax.

At the hotel in Cleveland where the Republican convention was held in the summer of 1936, the band played "Oh, Susanna" in honor of Kansas and Landon an estimated 800 times.

He was nominated on the first ballot.

In 1936, some viewed Landon, the admirer of Teddy Roosevelt, as perhaps a Republican New Dealer. From Topeka he made four major campaign swings around the country. On the first three, his attacks on the administration of Franklin D. Roosevelt were viewed as relatively mild.

On the last, he took the gloves off. In a speech in Baltimore, he asserted that "it is the essence of the New Deal that the Constitution must go in order to give men in Washington the power to make America over, to destroy the American way of life, and establish a foreign way in its place."

But in Landon's words, "There was only one time in that 1936 campaign when I thought I might beat Roosevelt."

That was when he learned the results of a straw poll taken by the Literary Digest, a publication now remembered mainly for making one of the major blunders in the history of public opinion surveys.

The Digest foresaw a Landon victory.

"For an hour or so that night," Landon said, "I could see myself in the White House."

But on Nov. 3, 1936, the voters gave Roosevelt 27,747,636 votes to Landon's 16,679,543.

Landon reacted calmly. He went duck hunting.

He served out his term as governor and retired from electoral politics.

For more than 50 years after the election, he lived in a white-columned house filled with books on a hillside at the edge of Topeka.

Bitterness, he said, never intruded. "You see," he once told an interviewer, "I had never planned a political career. With me, politics was not a vocation but an avocation."