This paper presents an algorithm for noninvasive estimation of alveolar pressure in mechanically ventilated patients who are spontaneously breathing. Continual monitoring of alveolar pressure is desirable to prevent ventilator-induced lung injury and to assess the intrinsic positive end-expiratory pressure (PEEPi), which is a parameter of clinical relevance in respiratory care and difficult to measure noninvasively. The algorithm is based on a physiological model of the respiratory system and, as such, it also provides insight into the respiratory mechanics of the patient under mechanical ventilation. In particular, the algorithm allows one to correctly estimate other clinical parameters of interest such as the patient's respiratory resistance and elastance, even in the presence of PEEPi.