Radford, 25, joined Sussex 13 months ago after two years with Middlesex but has made only five Championship appearances, scoring 34 runs.
Thursfield, also 25, spent five years with Hampshire before joining Sussex in the close season but has played in only two first-class games.
Tony Pigott, the chief executive, said: "We felt neither player was ever going to be a regular in the first team. It is better that they have the opportunity now to find another county during the season."
Worcestershire have awarded the former England seamer Phil Newport a benefit in 1998. Newport, 34, made his debut in 1982 and has taken more than 1,000 wickets.
Dave Gilbert, the Surrey manager, is calling for the 2nd XI Championship to be scrapped in its current format. Gilbert wants the number of games reduced and matches to be extended from three to four days.
The Australian, who will lead Surrey into Saturday's Benson and Hedges Cup final against Kent, believes the current system is of little benefit.
Gilbert said: "To play 17 three-day 2nd XI Championship matches each season is a joke and as the competition stands at present it should be scrapped.
"Three-day cricket no longer exists at first-team level and it's silly that it continues at second-team level. It often leads to contrived finishes and that doesn't teach anyone anything."
NATWEST TROPHY Quarter-final draw: Glamorgan v Yorkshire; Nottinghamshire v Essex; Derbyshire v Sussex; Middlesex v Warwickshire. (Matches to be played Tuesday, 29 July).Reuse content