The Association runs four team cup competitions over the summer months:

• The Chapman Cup is open to all and is run on a knock-out basis, with a handicap element.
• The Birstall Cup is the plate competition to the Chapman Cup.  It is open to first round losers from the Chapman Cup and is run on the same handicap basis.
• The Harrod Cup is a 5-round team rapidplay swiss event, open to teams whose players have an average grade no more than 125.
• The Wylie Cup is also a 5-round team rapidplay swiss event (or as the case may be, a round-robin event), open to teams whose players have an average grade no more than 162½.