Within occupational health research, one of the most influential models is the Job Demands-Control-Support model. Numerous studies have applied the model to different domains, with both physical and psychological health outcomes, such as burnout. The twin design provides a unique and powerful research methodology for examining the effects of environmental risk factors on burnout while taking familial factors (genetic and shared environment) into account. The aim of the present study was to investigate the impact of familial factors on the associations of burnout with job demands, control and support. A total of 14 516 individuals from the Swedish Twin Registry, who were born between 1959 and 1986, and who participated in the Study of Twin Adults: Genes and Environment (STAGE) by responding to a web-based questionnaire in 2005, were included in the analyses. Of these, there were 5108 individuals in complete same-sex twin pairs. Co-twin control analyses were performed using linear mixed modeling, comparing between-pairs effects and within-pair effects, stratified also by zygosity and sex. The results indicate that familial factors are of importance in the association between support and burnout in both women and men, but not between job demands and burnout. There are also tendencies towards familial factors being involved in the association between control and burnout in men. These results offer increased understanding of the mechanisms involved in the associations between work stress and burnout.