This paper presents a method for breath-by-breath noninvasive estimation of respiratory resistance and elastance in mechanically ventilated patients. For passive patients, well-established approaches exist. However, when patients are breathing spontaneously, taking into account the diaphragmatic effort in the estimation process is still an open challenge. Mechanical ventilators require maneuvers to obtain reliable estimates for respiratory mechanics parameters. Such maneuvers interfere with the desired ventilation pattern to be delivered to the patient. Alternatively, invasive procedures are needed. The method presented in this paper is a noninvasive way requiring only measurements of airway pressure and flow that are routinely available for ventilated patients. It is based on a first-order single-compartment model of the respiratory system, from which a cost function is constructed as the sum of squared errors between model-based airway pressure predictions and actual measurements. Physiological considerations are translated into mathematical constraints that restrict the space of feasible solutions and make the resulting optimization problem strictly convex. Existing quadratic programming techniques are used to efficiently find the minimizing solution, which yields an estimate of the respiratory system resistance and elastance. The method is illustrated via numerical examples and experimental data from animal tests. Results show that taking into account the patient effort consistently improves the estimation of respiratory mechanics. The method is suitable for real-time patient monitoring, providing clinicians with noninvasive measurements that could be used for diagnosis and therapy optimization.