Bronko Nagurski, whose great strength as a running back and tackler seemed to football fans of the 1920's and 1930's the epitome of bonecrushing power, died Sunday night at Falls Memorial Hospital in International Falls, Minn. He was 81 years old.

Mr. Nagurski, who became a charter member of the Pro Football Hall of Fame in 1963, had been in a nursing home for about a year and in the hospital for a week. The cause of death was not announced.

Bronislau Nagurski was born in Rainy River, Ontario, just over the United States border, to Ukrainian immigrants in 1908 and grew up in International Falls, Minn. He was given the nickname Bronko by his first teacher, who was unable to understand his mother's pronounciation of his first name.

He won all-America recognition from 1927 to 1929 at the University of Minnesota and in 1929 became the only football player to be honored as an all-American at two positions in a single season: defensive tackle and fullback.

Upon leaving Minnesota, he was signed in 1930 by George Halas, the owner and coach of the Chicago Bears of the National Football League, who saw him as a power runner to complement the outside scoring dashes of Red Grange.

Straight Downfield Runner

''I was a straight downfield runner; I wouldn't, or rather couldn't, dodge anybody,'' said Mr. Nagurski, who was known as a man who could run interference for himself. ''If somebody got in my way, I ran through them.''

He helped the Bears win championships in 1932 and 1933 and was voted All-Pro three times. He was paid $5,000 in his first season, but his salary then dipped for several seasons before rising again to $5,000. When when Mr. Halas refused to pay him $6,000 for the 1938 season, Mr. Nagurski retired and beame a professional wrestler.

''We used to say Coach Halas tossed nickles around like they were manhole covers,'' he recalled in a 1972 interview. ''People told me I could get into wrestling and make millions. I did it for about 12 or 14 years. It was tough work, and I didn't make millions.''

Comeback in 1943

After being rejected for military service during World War II because of damaged knees and ankles, Mr. Nagurski returned to the Bears for one last season in 1943, essentially as a defensive tackle, and again helped them to a championship.

Having gained 2,778 yards rushing in nine professional seasons as he played on both offense and defense, he once again retired and alternated between wrestling and operating a filling station near his home in International Falls. Following his retirement from wrestling in 1960, physical movement was so painful that he became a virtual recluse and he spent most of his time fishing, gardening or watching television.

''I want people to remember the way I was and not the way I am,'' he said.

Mr. Nagurski inspired stories akin to those about the legendary Paul Bunyan. He was supposedly recruited to play at Minnesota after the football coach, Clarence (Doc) Spears, saw him plowing in a field - without a horse. When asked directions, Mr. Nagurski, the story goes, pointed out the correct path while holding the plow in his hand.

Legendary Stories

On another occasion, an overflow crowd was kept under control by a squadron of mounted police. With the Bears near the goal line, Nagurski supposedly crashed into and through the end zone with such determined power that he knocked over one of the horses and its rider.

Perhaps the most familiar tale about the 6-foot-2-inch 230-pound Mr. Nagurski concerns a scoring run he made for the Bears at Wrigley Field. On a touchdown gallop against the Redskins, he is said to have knocked two linebackers in opposite directions, stomped over a defensive halfback and crushed an interferring safety man before caroming off the goalposts and finally crashing into the stadium's brick walls.

''That last guy hit me awfully hard,'' were the words attributed to him as he ran back to the huddle.

Mr. Nagurski seemed to lose most of his interest in football after his retirement.

''I sometimes think there is less enjoyment in the game now,'' he said in the early 1970's. ''The quarterback always handles the ball. The games all seem so much alike. Only the faces and numbers change. And of course, the platoons. We had 18 men on a team and you played 60 minutes, sometimes twice a week.

''If some of the big boys today played 60 minutes, they might not be so big. They'd sweat more.'' His survivors include four sons and two daughters, 15 grandchildren and one great-grandchild. Funeral services are scheduled for Saturday in International Falls.