A mechanistic model of the respiratory system is proposed to understand differences in quasistatic pressure-volume curves of the inflation process in terms of the alveolar recruitment and the elastic distension of the wall tissues. In the model, a total respiratory system consists of a large number of elements, each of which is a subsystem of a cylindrical chamber fitted with a piston attached to a spring. The alveolar recruitment is simulated by allowing a distribution of the critical pressure at which an element opens; while the wall distension is represented by the piston displacement. Relations are derived between parameters in the error-function model equation and properties of the mechanistic model. The parameters of the model-based equation are determined for clinical data sets of patients with acute respiratory distress syndrome.