This study examines the connections between children's sleep, stress, depression, and internet use. Parents believe that sleep effectively reduces children's stress, while children instead insist that internet use is effective for reducing their stress. Based on that argument, this study has three purposes: to examine whether sleep or internet use is more effective at reducing children's stress, examine whether stress is related to depression, and examine whether sleep affects depression through children's stress as a mediating factor. To this end, this study gathered a sample of 1,796 children from 32 elementary schools--all fourth- to sixth-graders who volunteered to take the survey--and measured their stress level, depression level, sleep hours, and hours of internet use. The Daily Stress Scale of Korean Children, Korean Child Depression Scale, hours of sleep on average per day (sleep), and hours of using electronic devices per day (internet use) were used as the measurements. Regarding the statistical analysis methods used in this study, linear regression was used to examine the regression effect of both sleep and internet use on stress and the regression effect of stress on depression. Path analysis, one of the structural equation models, was also used to find direct, indirect, and mediating effects between variables. The study results show that (i) sleep, not internet usage, effectively relieves children's stress; (ii) stress is an important influence on depression; and (iii) sufficient sleep reduces stress, which reduces depression. It is recommended that future studies consider the quality of sleep and quantity of sleep for more valid data analysis and carry out follow-up research with wider age groups.