Background The most common fractures in children are torus (buckle) fractures of the wrist. Controversy exists over treatment, which ranges from splint immobilisation and discharge to cast immobilisation, follow-up, and repeat imaging. This study compared pain and function in affected children offered a soft bandage and immediate discharge with those receiving rigid immobilisation and follow-up as per treating centre protocol. Methods In this randomised controlled equivalence trial we included 965 children (aged 4–15 years) with a distal radius torus fracture from 23 hospitals in the UK. Children were randomly allocated in a 1:1 ratio to the offer of bandage group or rigid immobilisation group using bespoke web-based randomisation software. Treating clinicians, participants, and their families could not be masked to treatment allocation. Exclusion criteria included multiple injuries, diagnosis at more than 36 h after injury, and inability to complete follow-up. The primary outcome was pain at 3-days post-randomisation measured using Wong-Baker FACES Pain Rating Scale. We performed a modified intention-to-treat and per protocol analysis. The trial was registered with ISRCTN registry, ISRCTN13955395. Findings Between Jan 16, 2019, and July 13, 2020, 965 children were randomly allocated to a group, 489 to the offer of a bandage group and 476 to the rigid immobilisation group, 379 (39%) were girls and 586 (61%) were boys. Primary outcome data was collected for 908 (94%) of participants, all of whom were included in the modified intention-to-treat analysis. Pain was equivalent at 3 days with 3·21 points (SD 2·08) in the offer of bandage group versus 3·14 points (2·11) in the rigid immobilisation group. With reference to a prespecified equivalence margin of 1·0, the adjusted difference in the intention-to-treat population was –0·10 (95% CI –0·37 to 0·17) and–0·06 (95% CI –0·34 to 0·21) in the per-protocol population. Interpretation This trial found equivalence in pain at 3 days in children with a torus fracture of the distal radius assigned to the offer of a bandage group or the rigid immobilisation group, with no between-group differences in pain or function during the 6 weeks of follow-up. Funding UK National Institute for Health and Care Research.