The latest, on Sunday, took place at around 7pm and saw yobs target the skate park on Pontefract Road.
A spokesperson for Barnsley Council said: “These mindless acts damage the local environment and ruin facilities for everyone as well as tying up fire crews, potentially slowing down their response to a more severe and life-threatening incident.
“The firefighters have even had verbal abuse from a group of young people as they were trying to put the fires out.
“For everyone’s benefit, we need to stop these fires and ask residents to come forward with any information on who may be setting these fires.
“If you have any information about this, please email email@example.com or call 773555.”
Steve Jones, manager of nearby Cudworth station, added: “Such mindless behaviour ties up our crews and means they may be slower to respond to a more serious incident.
“To anyone setting fires on purpose, how would you feel if your family were in a house fire and our response was delayed due to being stuck at a needless grass fire?”
The crew have also been victims of verbal abuse from groups in the area - with the trend of this increasing.
Steve added: “Our staff, much like other emergency services, dedicate their lives and careers to helping others and saving lives. We totally condemn anyone who chooses to abuse them in any way.
“Please, if you know anything about these incidents, report it to the police or our colleagues at Barnsley Council.
“Let’s keep our firefighters free for real, life-threatening emergencies.”