Background A surgical operation in pediatric patients is a rather stressful experience for both children and their parents. The aim of this study was to assess the effect of specific demographic characteristics in parent's and children's preoperative anxiety. Methods The sample was composed of 128 Greek-speaking children (1–14 years of age) who had to undergo minor surgery in a University General Hospital. Before surgical operation, the Spielberger State-Trait Anxiety Inventory (STAI) questionnaire and a questionnaire for the social-demographic characteristics were completed by the parents. Children's preoperative anxiety was evaluated using the Modified Yale Preoperative Anxiety Scale (m-YPAS). Results The independent predictors of increased anxiety levels in parents are child's age (p=0.024) and gender (girls: p=0.008), living in rural areas (parents: p < 0.001; children: p=0.009), being a mother (p=0.046), high or low education level (p=0.031), a no premedicated child (p=0.007), and high baseline parental anxiety (p=0.003). Previous hospitalization (p=0.019), high situational parental anxiety (p < 0.001), no premedication (p=0.014), and being the only child in the family (p=0.045) are found to be the main determinants of preoperative anxiety control in children. Conclusions This study identifies possible risk factors of preoperative anxiety in parents and their children, which are high parental anxiety, child's age, no premedication, being the only child in the family, living in rural areas, education level, and previous hospitalization.