Spontaneous breathing during mechanical ventilation is common in the neonatal intensive care unit. The breathing efforts in spontaneous breaths generate negative pressures in the pleural space, complicating model-based analysis due to unknown parameter tradeoff. This paper estimates the pleural pressure and elastance in a single compartment model applied to data from a neonate undergoing synchronous intermittent mandatory ventilation. Two sets of 60 breaths were analysed. Resistance is empirically modelled based on endotracheal tube dimensions. Breath-to-breath elastance is estimated from expiration data, assuming passive expiration, and inspiratory pleural pressure is modelled using B-spline functions. Typical breathing trends were observed, patient-triggered inspiration was apparent, and the work of breathing was significantly decreased in ventilator supported breaths compared to unsupported breaths. Additionally, examples of ventilator-patient asynchrony were observed when comparing pleural pressure to airway pressure. This study contributes to the development of computational models for respiration mechanics. The fundamental aim is to provide clinicians with more physiological insight and tools to improve neonatal ventilation support.