Although social integration of youths with intellectual disabilities improves their psychological adaptation, it nevertheless exposes them to a higher risk of stress. The author's goal was to verify the regulatory role of anxiety, respectively, as a trait and as a state in youth with mild intellectual disability who are coping with difficult situations. The study, involving a group of 120 students at the Education and Rearing Center in Kielce (Poland), used two psychological methods pertaining to a cognitive paradigm. The first was the State‐Trait Anxiety Inventory (ISCL—Polish version of STAI) and the other was the self‐description technique of the authorship “That's Life,” devised with the aim of revealing either task strategies or emotional and avoidant strategies adopted by the respondents. The tools are matched to specific cognitive abilities and social experiences typical of youth with mild intellectual disability. Correlative research model was applied. The results of linear regression and variance analyses showed the regulatory role of the state anxiety for youth with mild intellectual disability with reference to coping strategies. A higher intensity of anxiety stimulated their defensive activity, especially in the context of ambivalent conflicts, whereas a decrease in state anxiety led to their employing task‐focused strategies. The results should encourage the development and application of anxiety‐reducing techniques based on cognitive confrontation to activate task‐oriented coping.