A method of measuring the instantaneous arterial blood pressure and compliance and the device thereof are disclosed. The method identifies a critical depth under the skin. At this critical position, the arterial mean blood pressure is equivalent to the mean blood pressure obtained on the skin. The variation in the arterial mean blood pressure is tracked and controlled to maintain the equivalence between the mean blood pressure measured on the skin and the arterial mean blood pressure. In this case, the compliance of the muscle tissues remains invariant. Therefore, the variation measured on the skin is simply the behavior of the blood vessel. Using the skin-artery correlation, the invention can obtain the instantaneous blood pressure after some computation and the dynamic compliance at the critical position.