Complete Sectional Qualifying Results
This year's U.S. Open will be conducted at Southern Hills Country Club in Tulsa, Oklahoma from June 14-17.
Strange, who won the Open in 1988 and '89, struggled to a 36-hole total of five-over 147 (79-68) at Colonial Country Club in Memphis, Tennessee -- one of four qualifying sites on Tuesday. Simpson was three shots worse at eight-over 150 (76-74).
Brian Henninger led the field of 135 in Memphis, the site of this week's PGA Tour stop, with a two-round total of 11-under 131. A total of 29 spots were available in Memphis. Rich Beem, Dan Forsman, Jeff Maggert and Paul Goydos were among those who also qualified in Memphis.
Other prominent PGA Tour players failing to qualify at the Memphis site included Steve Elkington, Craig Parry and Jeff Sluman.
Five spots for 81 players were available at Old Oaks Country Club in Purchase, New York. Tim Petrovic had the low score at 138, while Jim McGovern, Michael Allen, George Frake and Scott Dunlap also qualified. Dunlap won a five-man playoff that involved 1984 Open champion Fuzzy Zoeller for the final spot.
Wes Heffernan and Scott Johnson earned the two spots available at the TPC of Snoqualmie Ridge in Washington.
Qualifying at Old Memorial Golf Club in Tampa was suspended late in the afternoon because of weather conditions. Play will resume there on Wednesday morning.
Qualifying was also held on Monday at nine sites around the country.