Richardson, the 2001 champion, beat Jim Lipe, of Shreveport, La., 4 and 3 in the second round and Beecher Metzger, of Venice, Fla., 3 and 2 in the third round.
'It's a long day, especially when you are walking the place,' said Richardson, a stockbroker from Laguna Niguel, Calif. 'But I played well. I'm driving it well.'
Edward Craig, of Orlando, Fla., defeated Bill Ploeger, of Columbus, Ga., the 1999 champion and 2001 runner-up, 1 up in the third round.
Craig, a small jet pilot, won three of the first four holes and never trailed.
'I knew I had to start out quickly because his reputation precedes him,' Craig said of Ploeger.
Bob Hullender, the 1994 runner-up from San Antonio, Texas, defeated 2002 runner-up Mark Bemowski, of Mukwonago, Wis. in the third round.
Hullender, a retired Air Force general, was 4 up through seven holes and then lost five of the next seven holes to birdies by Bemowski.
Hullender birdied 16 and 17 to retake the lead. He drained a long birdie putt on 18, while Bemowski missed a 4-footer for eagle.
Others advancing to Wednesday's quarterfinalists were: Frank Abbott, of Napa, Calif.; David Boesel, of Winter Park, Fla.; Sam Farlow, of Birmingham, Ala.; third-seeded Bruce Richards, of Bellevue, Wash.; and 2003 British Senior Amateur champion Roy Smethurst, of England.
The semifinals will also be played Wednesday at the 6,914-yard Virginian Golf Club. The final is Thursday.