Cancer genomics has revealed many genes and core molecular processes that contribute to human malignancies, but the genetic and molecular bases of many rare cancers remains unclear. Genetic predisposition accounts for 5 to 10% of cancer diagnoses in children and genetic events that cooperate with known somatic driver events are poorly understood. Pathogenic germline variants in established cancer predisposition genes have been recently identified in 5% of patients with the malignant brain tumour medulloblastoma. Here, by analysing all protein-coding genes, we identify and replicate rare germline loss-of-function variants across ELP1 in 14% of paediatric patients with the medulloblastoma subgroup Sonic Hedgehog (MBSHH). ELP1 was the most common medulloblastoma predisposition gene and increased the prevalence of genetic predisposition to 40% among paediatric patients with MBSHH. Parent-offspring and pedigree analyses identified two families with a history of paediatric medulloblastoma. ELP1-associated medulloblastomas were restricted to the molecular SHHα subtype4 and characterized by universal biallelic inactivation of ELP1 owing to somatic loss of chromosome arm 9q. Most ELP1-associated medulloblastomas also exhibited somatic alterations in PTCH1, which suggests that germline ELP1 loss-of-function variants predispose individuals to tumour development in combination with constitutive activation of SHH signalling. ELP1 is the largest subunit of the evolutionarily conserved Elongator complex, which catalyses translational elongation through tRNA modifications at the wobble (U34) position. Tumours from patients with ELP1-associated MBSHH were characterized by a destabilized Elongator complex, loss of Elongator-dependent tRNA modifications, codon-dependent translational reprogramming, and induction of the unfolded protein response, consistent with loss of protein homeostasis due to Elongator deficiency in model systems. Thus, genetic predisposition to proteome instability may be a determinant in the pathogenesis of paediatric brain cancers. These results support investigation of the role of protein homeostasis in other cancer types and potential for therapeutic interference.