Scotland host Georgia on October 11 at Ibrox, before they travel to Warsaw to take on Poland three days later as they go in search of their first points in Group D following a spirited 2-1 defeat at world champions Germany in their opening fixture.
Strachan has included Gauld in his 27-man party for the two games, with the 18-year-old yet to feature for Sporting Lisbon's first team this season since a move from Dundee United in June.
May, who moved south of the border from St Johnstone to join Sheffield Wednesday during the off-season, has netted three goals in eight Championship appearances so far.
Both men have Under-21 caps for their country, while Scotland are further boosted by the return of Celtic's Scott Brown after a hamstring injury.
Squad in full:
Goalkeepers: Craig Gordon (Celtic), David Marshall (Cardiff City), Allan McGregor (Hull City) Defenders: Christophe Berra (Ipswich Town), Craig Forsyth (Derby County), Gordon Greer (Brighton and Hove Albion), Grant Hanley (Blackburn Rovers), Alan Hutton (Aston Villa), Russell Martin (Norwich City), Mark Reynolds (Aberdeen), Andrew Robertson (Hull City), Steven Whittaker (Norwich City) Midfielders: Ikechi Anya (Watford), Barry Bannan (Crystal Palace), Scott Brown (Celtic), Craig Bryson (Derby County), Chris Burke (Nottingham Forest), Graham Dorrans (West Bromwich Albion), Darren Fletcher (Manchester United), Ryan Gauld (Sporting Lisbon), Shaun Maloney (Wigan Athletic), James McArthur (Crystal Palace), James Morrison (West Bromwich Albion) Forwards: Steven Fletcher (Sunderland), Steven May (Sheffield Wednesday), Chris Martin (Derby County), Steven Naismith (Everton)