The maximum elastance of the ventricle (Emax) is a strong candidate for a quantitative index used for determination of the timing of weaning the patient from a left ventricular assist device (LVAD). This paper presents a new and less invasive method for deriving Emax of the left ventricle under the LVAD assistance. In this method (the CoP method), Emax can be calculated from two different end-systolic points which are produced by changing the drive phase of LVAD without any vascular clamping and any direct measurement of the left ventricular volume. Animal experiments indicated that the CoP method is useful when the measured left ventricular flow and pressure are employed. Moreover, a new technique for estimating the left ventricular flow was developed to make the CoP method less invasive without direct measurement of the flow. The technique could considerably improve the estimation accuracy of the flow in the co-pulsation mode in comparison with the previous one proposed by the authors. However, it has been revealed that the estimation accuracy of the left ventricular flow was not globally high enough to apply the CoP method to clinical cases in spite of its much less invasiveness.