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The non-coding space makes up around 98 % of the genome, but cancer-driving mutations have so far mostly been discovered in protein-coding regions. The majority of somatic non-coding mutations are neutral passenger mutations and identifying non-coding mutations with driving roles in cancer poses a challenge. In this work, evolutionary constraint was used to explore the non-coding space in human osteosarcoma to improve our understanding of how evolutionary constraint can be applied to identify non-coding driver mutations in cancer and describe the unknown role of non-coding mutations in osteosarcoma. Evolutionary constraint scores derived from an alignment of 33 mammals were used to extract non-coding mutations in functional elements from somatic variants of 38 osteosarcoma samples and genes with an enrichment of non-coding constraint mutations in their regulatory regions were identified. The investigation of those genes revealed that non-coding constraint mutations are likely involved in key osteosarcoma pathways. Furthermore, novel osteosarcoma genes and mechanisms were proposed based on the non-coding constraint mutation enrichment analysis. The regulatory potential of individual non-coding constraint mutations was evaluated based on regulatory annotations, functional evidence, transcription factor affinity predictions and electrophoretic mobility shift assays. We concluded that the analysis of non-coding constraint mutations is an efficient way to discover non-coding mutations with functional impact in osteosarcoma which likely play an important role in the disease.