Dick Radatz, whose towering presence and 95-mile-per-hour fastball made him baseball's most dominant relief pitcher in the mid-1960s and earned him the unforgettable nickname of "The Monster" in Red Sox lore, died yesterday when he fell down a flight of stairs in his home in Easton, according to police.

The 6-foot-5-inch Mr. Radatz, who would have turned 68 April 2, lost his balance and suffered a severe head injury in the fall, according to Easton Police Chief Thomas Kominsky.

"It is believed that as Radatz tumbled down the stairs, he struck his head on the carpet-covered concrete floor," Kominsky said in a statement. ''Paramedics were unable to revive Radatz, due to the severity of his injuries -- severe head trauma."

The cause of death is believed to be accidental, Kominsky said. He said the offices of the state medical examiner and Bristol County district attorney were investigating.

Mr. Radatz spent the last two years as pitching coach for the Lynn-based North Shore Spirit, an independent minor league team, and he was planning to return this spring, according to Spirit manager John Kennedy, the former Red Sox infielder, even though Mr. Radatz's considerable girth -- his weight approached 400 pounds -- made trips to the mound a rarity.

Mr. Radatz missed the Red Sox fantasy camp in Florida last month after undergoing surgery on a leg earlier this winter.

''Just above his ankles and below both knees his legs were all discolored," Kennedy said last night. ''I was concerned he might lose a leg. It would be purple and dark purple and one time I saw him it was almost black."

''He was a good guy, a lot of laughs."

Born in Detroit on April 2, 1937, Richard Raymond Radatz was a baseball and basketball star at Michigan State before signing with the Red Sox in 1960.

He was still in the minor leagues when he developed a sore arm and begged his manager at the time, Johnny Pesky, not to send him to the bullpen. But it was as a relief pitcher that Mr. Radatz made it to the big leagues in 1962, and in the span of the next five seasons, he was the biggest star on a series of bad Sox teams. His trademark gesture of thrusting his fists into the air as he made his way off the mound, victorious, was as familiar to one generation of Sox fans as Nomar Garciaparra's toe-tapping would become for a more recent generation.

''He was the best," said former Sox teammate Bill Monbouquette, reached last night by phone in Lakeland, Fla., where he is a minor league pitching coach for the Detroit Tigers. ''How would I say the best? When you compare him to other guys, they couldn't do what he did. Three innings one day, maybe four the next, one the next day, and three more the next.

''Relievers today throw one inning. Dick almost never pitched just an inning."

In one memorable two-game span, Mr. Radatz pitched 15 innings, 6 in one game, then 9 of an extra-inning game the next night.

''I never used to give the ball to the manager when he'd come to get me," Monbouquette said. ''I'd wait to give it to the guy coming into the game. I used to say to Dick, 'You'd better get these guys out or I'm going to kick your [butt],' He'd say, 'Go in the clubhouse, crack me a Bud, and I'll be right up.' And he would.' "

''The Monster" nickname was born in 1963, after a game against the Yankees in Fenway Park in which Mr. Radatz entered with the bases loaded and struck out Mickey Mantle, Roger Maris, and Elston Howard -- all American League MVPs at one time -- on a total of 10 pitches.

It was after that game that Mr. Radatz punched the sky, a gesture he forgot about making until legendary Sox broadcaster Curt Gowdy reminded him of it the next day.

Mantle, the story goes, was heard to grumble about ''that monster" afterward, and a nickname was born. Newspaper reports say Mr. Radatz faced Mantle, a Hall of Famer, 63 times, and struck him out 47 times.

''Mickey used to say, 'Damn it, I know what he's going to throw and I still can't hit it," Monbouquette said. ''I think he hit one home run off Dick, in Yankee Stadium, and I think Dick broke his bat.

''Just to watch him, you knew you had no chance against him," Monbouquette said. ''He had no offspeed pitch, but he threw 95, 96, he had great location and he'd come right at you, get you 0 and 2 and just blow you away. He was a pure power guy."

Mr. Radatz won or saved 33 of Boston's 76 wins in 1962; 40 of Boston's 76 wins in 1963; 45 of Boston's 72 wins in 1964; and 31 of Boston's 62 wins in 1965. He led the American League in saves in 1962 and 1964 and made the All-Star team in 1963 and 1964.

He ranks second on the Sox all-time list of saves leaders with 104.

But a puzzling drop in velocity and ineffectiveness led to Mr. Radatz being traded to the Cleveland Indians in 1966, and in the next three seasons he bounced among three other teams -- the Cubs, Tigers and Expos -- before his career came to an end in 1969.

Funeral arrangements had not been announced last night.

Among his survivors, Mr. Radatz had a son, Dick Jr., who runs a collegiate baseball league in Michigan, and a daughter.