1. An apparatus for analyzing elastography of tissue using a one-dimensional (1D) ultrasound probe with transducers arranged along a single dimension, the apparatus comprising: an ultrasound image processor for acquiring two-dimensional (2D) ultrasound images with respect to a region of interest (ROI), of an object to be diagnosed, in which an asymmetric shear wave is induced using the 1D ultrasound probe; and a processor configured to: measure a displacement of the asymmetric shear wave from the acquired 2D ultrasound images; estimate a change rate in the displacement of the asymmetric shear wave along a y-axis direction orthogonal to a 2D plane in which the 2D ultrasound images acquired by the ultrasound image processor are shown, using the measured displacement; analyze elastography information of tissue in the ROI using the measured displacement and the estimated displacement change rate; generate an elastographv image of the ROI using the elastographv information; and control a display to display the elastography image.