An apparatus for determining an instantaneous elastic recoil pressure during the provision of respiratory assistance, comprises: an air supply means controllable to supply breathable air to a subject's airway continually at a selectable pressure elevated above atmospheric pressure as a function of an instantaneous elastic pressure; a flow sensor means to generate a flow signal representative of respiratory airflow; and a processor means to process a flow signal from said flow sensor and to control said air supply means, wherein said processor is programmed to:receive as input an elastance value for a subject;calculate an index value representing an extent to which any leak is suddenly changing using sampled flow values from said flow signal;calculating an inspired volume of airflow as a function of said measure of respiratory airflow and said index value; andcalculating said instantaneous elastic recoil pressure as a function of said inspired volume and said elastance value.