Church Stretton Town Council says an attempt was made to set fire to a bin on Tuesday before the team spotted signs of damage and graffiti on Wednesday.
A spokesperson for the town council said on social media that the issues have been reported to the police.
"The town council's outdoor team were saddened to have found vandalism in the Town Park when they arrived at work on Wednesday morning," they wrote on Facebook.
"An attempt was also made to set fire to a bin on Tuesday during the day."
They said it was causing more work for a stretched council team who take pride in maintaining Town Park.
" Although this may be seen as entertainment for some, it is simply causing more work for an already stretched team who take a lot of pride in maintaining our Town Park," said the spokesperson.
"All matters have been reported to the police.
"But please could we ask if you see any vandalism taking place, not to approach anyone, but to report the issue. Thank you."