Disclosed is an ultrasound apparatus. The ultrasound apparatus includes an ultrasound transceiver that transmits an ultrasound signal to an object and receives an ultrasound echo signal reflected from the object, a controller that detects a change amount of a diameter of a blood vessel of the object, based on the ultrasound echo signal, and a display unit that displays a blood pressure graph showing a blood pressure of the object and an image representing an inflection point in the blood pressure graph, based on the detected change amount of the diameter. The controller calculates a stiffness of the blood vessel, based on a blood pressure corresponding to the inflection point.