An analytical mathematical model of a stentless aortic valve has been implemented. The valve is characterised by a trileaflet geometry, cylindrical leaflets; the aortic root is schematised by a conical surface which includes the leaflet attachments. The model is defined through six geometric parameters: the base radius, the valve height, the commissure radius, the leaflet radial, circumferential and attachment line lengths. Five performance indexes have been used to optimise the valve geometry, namely: the systolic area, the leaflet circumferential stress in diastole, the leaflet bending strain in systole and two bending angles related to the rotation of the leaflets from the diastolic to the systolic configuration. The sensitivity analysis is carried out which can identify the influence of each geometric parameter on the performance indexes adopted for the optimum valve design. The analysis of the results provides the geometric configuration which optimises the overall function of the valve throughout the cardiac cycle.