The study presents an automated algorithm for analyzing airways from CT scans of cystic fibrosis patients. The framework consists of two stages: the first extracts and skeletonizes the airway tree, while the second measures airway volume, branch count, generation splits, diameters, and cross-sectional areas. The analysis was performed on 169 CT volumes from patients aged 6 to 18 years. Results showed significant differences between the control group and cystic fibrosis patients in the number of detected branches, generation splits, and normalized airway volume. Cystic fibrosis patients demonstrated an increased number of small airways due to early bronchiectasis. The algorithm enables accurate quantification of airway changes that vary with disease severity or treatment.