Three bikes, which police say were not roadworthy, also sped by schoolchildren on Gibbons Road. Trench. shortly after 3pm on Tuesday.
Police tried to speak to the riders but the vehicles did not stop.
One of the bikes is described as a green and black mini off-road motorcycle, the other was a blue off-road mini bike and the third was a red motorcycle being rode by a man, thought to be in his late 20s with a beard.
West Mercia Police has released two images of the vehicles they are searching for.
A police spokesman said: "As the children were leaving a local primary school, three off-road motorcycles were riding at speed on Gibbons Road, none of which were fit for the road.
"Officers tried to stop them but they sped past with no regard for the officers' safety or the public.
"Bike one was a green and black mini off-road motorcycle. Bike two was a blue off-road mini bike with an extended rear swinging arm as shown in the image. Bike three was a red bike with an adult male, late 20s, beard.
"Please note the distinctive jacket and gloves on the rider of the red bike."
Schools in the area include Wrockwardine Wood Infant School, Wrockwardine Wood Junior School, St Luke's Catholic Primary School and Telford Priory School.
Anyone with information can contact West Mercia Police on 101 or at email@example.com
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org