A seam bowler who could move the ball both ways, he was also an exceptionally hard-hitting late- order batsman who could always be relied on to pick up valuable runs for his side.
In a Sunday League match at Middlesbrough in 1984, he smashed 81 not out off 29 balls against Somerset, including 10 sixes. So fierce were his shots that those in the Press box had to keep taking evasive action, while one of the sixes went straight through the window of the box occupied by scorer Ted Lester.
Stevenson was also noted for his fielding and his bullet-like returns from the boundary edge which would land straight in the wicketkeeper’s gloves.
He played in 177 first class matches for Yorkshire between 1973 and 1986, taking 464 wickets, scoring 3,856 runs with two centuries and holding on to 73 catches.
He also played in two Test matches for England and represented his country in four one-day internationals.
He was one of the county’s most popular figures, both with team-mates and spectators. He was admired by his former captain and friend, Geoffrey Boycott, who often admitted that Stevenson was one of his favourite cricketers.
Boycott was an early mentor who arranged for him to attend nets at Headingley when he was a youth. But for him, Stevenson might have become a footballer as he had trials at about the same time with Sheffield Wednesday, of whom he was a supporter, and Doncaster.
Graham Barry Stevenson was born in Ackworth, near Wakefield. He was raised by his grandparents, Dick and May Stevenson, and was educated at Minsthorpe High School, Wakefield.
He was an entertaining player, especially in one-day matches, who might have gone on to greater things if it had not been that he developed as a first-class cricketer at the same time as Ian Botham.
He played in 216 limited overs games for Yorkshire, taking 290 wickets and scoring 1,699 runs.
Had he been playing today he would have been a strong asset to any side in Twenty20 cricket and would probably have made a big name for himself in the game.
It was with the ball that he made his most important contributions for his county. Against Northamptonshire at Headingley in 1980, he took the first eight wickets at a cost of 57, and might have gone on to bag all 10 if he had not left the field to change his shirt.
In 1978 he was the scourge of arch rivals Lancashire, destroying them in their first innings at Headingley with figures of 8 for 65, Yorkshire going on to win by an innings and 32 runs on the second day.
At Old Trafford later in the season, Yorkshire won by 10 wickets after Lancashire were destroyed by Stevenson, who took 5 for 61 and 3 for 57, and his new-ball partner Chris Old who scored an unbeaten century and took 4 for 38 and 5 for 47.
But perhaps one of his most memorable acts was with the bat when he shared a Yorkshire record-breaking last wicket stand of 149 with Boycott against Warwickshire at Edgbaston.
As the last man in, Stevenson thrashed 115 not out, which at the time was the highest unbeaten score ever recorded by a No 11 batsman.
He made his Test debut against India at Bombay in February, 1980 having flown out to join the tourists as replacement for Derbyshire’s seam bowler Mike Hendrick.
Stevenson’s second, and last Test appearance ,was against the West Indies in Antigua during the following winter tour.
He made a storming one-day international debut against Australia at Sydney in January 1980 taking 4 for 33 and scoring 28 off 18 balls, helping England to win by two wickets.
His last one-day appearance was in February 1981 against the West Indies.
Sadly, he left Yorkshire in 1986 feeling hurt that he had not been awarded the traditional Benefit which players in those days relied on financially when they finished playing. He took a long time to come to terms with his disappointment.
He then had one season with Northamptonshire before taking a variety of jobs to support his young family, including working as a scaffolder, a bailiff and a milkman.
In 1977 he married his wife, Angela, whom he had known since they were 11. Both had grown up in Ackworth, where the family has continued to live.
He is survived by his wife, his son Christopher, daughter Cheryl and grandsons George and Jacob.