Summary Background Hidradenitis suppurativa (HS) is a recurrent inflammatory skin disease that, apart from rare causative loss-of-function mutations, has a widely unknown genetic aetiology. Objectives To estimate the relative importance of genetic and environmental factors underlying susceptibility to HS. Methods Via the Danish Twin Registry and the Danish National Patient Registry we pulled together information on zygosity with that of HS status. Cases of HS were identified by the International Classification of Diseases (ICD)-8 (705·91) and ICD-10 (L73·2). Heritability was assessed by the classic biometric model and the possibility of gene–gene interaction via the multilocus modelling approach. Results Among 100 044 registered twins, we found 170 twins (from 163 pairs) diagnosed with HS. The seven concordant pairs were all monozygotic. Monozygotic twins had a case-wise concordance rate of 28% [95% confidence interval (CI) 7–49], corresponding to a familial risk of 73 (95% CI 13–133) times that of the background population. The biometrical modelling suggested a heritability of 0·80 (95% CI 0·67–0·93), and the multilocus index estimate was 230 (95% CI 60–400). This is highly indicative of gene–gene interactions, with the possibility of up to six interacting loci. Conclusions This twin study was substantially larger and employed a more valid phenotype than previous studies. Genetics account for the majority of HS susceptibility, and HS is most likely caused by gene–gene interactions rather than monogenetic mutations or solely additive genetic factors. New approaches aimed at assessing potential interactions at a single-nucleotide polymorphism (SNP)–SNP level should be implemented in future HS genome-wide association studies.