Predictions of individualized models of respiratory mechanics provide insight into the patient state. Therefore, they may help to reduce the potentially harmful effects of ventilation therapy for Acute Respiratory Distress Syndrome (ARDS) patients. To assure bedside-applicability, the underlying model has to be computationally efficient while capturing dominant dynamics observed and also be identifiable from the available data. In this work, a recruitment model is enhanced by considering alveolar distension effects and implemented in a time-continuous respiratory mechanics model. The model is used to identify patient-specific models for 12 ARDS patients from a previous study using a gradient-based parameter identification method. Appropriate initial values for parameter identification are hierarchically derived by identifying simpler models first. The reported parameter values were physiologically plausible and capable of reproducing the measured pressure with high accuracy. The presented model provides timecontinuous simulations of airway pressure, is physiologically relevant term by term, uses clinically descriptive parameters and captures dominant ARDS dynamics. The patient-specific models also capture pulmonary dynamics for clinical guidance that are currently not directly measurable without such a validated model.