Objective. To assess the factors related to perioperative state anxiety in paediatric patients and their parents. Methods. A cohort study was conducted on paediatric patients 9–17 years of age, who underwent the modified Ravitch procedure (n = 96), and their parents (n = 96). The level of anxiety was measured using the State-Trait Anxiety Inventory questionnaire. Multivariable linear regression models were calculated to find the relationships between the pre- and postoperative state anxiety of the patients/parents and the independent variables, both demographic (age, gender) and clinical (e.g., postoperative pain, trait anxiety). Results. Preoperative anxiety in the paediatric patients was positively correlated with their trait anxiety (β = 0.47; 95% CI: 0.29 to 0.64) and preoperative parental anxiety (β = 0.24; 95% CI: 0.07 to 0.42). The high level of preoperative anxiety (vs. low and moderate) (β = 0.40; 95% CI: 0.22 to 0.58), trait anxiety (β = 0.22; 95% CI: 0.04 to 0.40) and average postoperative pain at rest (β = 0.18; 95% CI: 0.01 to 0.34) had a positive impact on the postoperative anxiety in patients. However, the patients’ age was negatively correlated with postoperative anxiety (β = −0.19; 95% CI: −0.35 to −0.02). Three variables were found to predict preoperative parental anxiety: their trait anxiety (β = 0.41; 95% CI: 0.23 to 0.59), female gender (β = 0.18; 95% CI: 0.002 to 0.36) and the intravenous route for the postoperative pain management in the patients (β = −0.18; 95% CI: −0.36 to −0.001). The parental postoperative anxiety was influenced by their trait anxiety (β = 0.24; 95% CI: 0.04 to 0.43), preoperative anxiety in patients (β = 0.21; 95% CI: 0.02 to 0.40) and female gender of children (β = 0.19; 95% CI: 0.001 to 0.39). Conclusions. Trait anxiety was a strong factor positively affecting the perioperative state anxiety. In addition, paediatric patient anxiety before surgery was related to their parents’ anxiety, and, after surgery, this was associated with high preoperative anxiety, pain and age. The parents’ anxiety before surgery was influenced by gender and the type of postoperative analgesia in the patients, while, after surgery, this was influenced by the patients’ preoperative anxiety/gender.