METHODS AND DESIGN: The CURE RCT compares two groups of patients requiring invasive MV with a partial pressure of arterial oxygen/fraction of inspired oxygen (PaO2/FiO2) ratio ≤ 200; one criterion of the Berlin consensus definition of moderate (≤ 200) or severe (≤ 100) ARDS. All patients are ventilated using pressure controlled (bi-level) ventilation with tidal volume = 6-8 ml/kg. Patients randomised to the control group will have PEEP selected per standard practice (SPV). Patients randomised to the intervention will have PEEP selected based on a minimal elastance using a model-based computerised method. The CURE RCT is a single-centre trial in the intensive care unit (ICU) of Christchurch hospital, New Zealand, with a target sample size of 320 patients over a maximum of 3 years. The primary outcome is the area under the curve (AUC) ratio of arterial blood oxygenation to the fraction of inspired oxygen over time. Secondary outcomes include length of time of MV, ventilator-free days (VFD) up to 28 days, ICU and hospital length of stay, AUC of oxygen saturation (SpO2)/FiO2 during MV, number of desaturation events (SpO2