Only 11.3 overs play was possible at Grace Road for the LV= County Championship Division Two clash as Yorkshire advanced to 382 for six against Leicestershire with Adam Lyth still there on 179.
A 45-minute break was followed at 12.30 by a seven-ball session which was swiftly terminated when another shower swept across the ground.
Anthony McGrath failed to add to his overnight total of eight after being caught low by Greg Smith at slip off Matthew Hoggard's first ball of the day. Aside from Lyth, Yorkshire's highlight has been a stylish innings from Azeem Rafiq who is 23 not out as the teams finished early for lunch.
Kent, meanwhile, added 75 to their overnight total with the loss of just Mark Davies on 17 who was caught by Hampshire's Dimitri Mascarenhas off James Tomlinson's delivery.
Kent were on 366 for six as they went into lunch at the Rose Bowl.