Introduction: Constructive coping strategies play an important role during childcare processes. We examined the determinants of coping strategies used by parents raising children with intellectual disabilities or other developmental disorders and by parents with typically developing children. Methods: The cross-sectional study was carried out in Cracow. The participants in the survey were 507 caregivers. The research used the Mini-COPE Inventory for Measurement-Coping with Stress and the General Self-Efficacy Scale. Results: Parents of disabled children and parents of children without disabilities used the strategy of active coping most often and the strategy of substance use the least. Sociodemographic variables such as age, place of residence, education, and sociodemographic situation determined the type of strategy for dealing with stress. The statistical analysis showed the relationship between parents' self-efficacy and type of coping strategy. Conclusion: There is a need to develop individualized family psychological support programs to stimulate caregivers' constructive coping strategies.