An analysis of assisted respiration, based on a linear, first-order lung model, has been performed using rectangular, sine and ramp input pressure waveforms. The results of the analysis have been applied to predict optimal respirator settings. The criterion of a simultaneous minimisation of the average alveolar pressure and ventilatory work per minute has been used for designing the respirator. The choice of the input pressure waveform is optimised on the basis of minimum work done by the patient. Respirator design parameters have been presented for normal adults with varying degrees of spontaneous effort, respiratory rate and rectangular, sine and ramp input pressure waveforms. The designs can be readily modified for patients with a variety of respiratory diseases.