We propose a method of using ultrasonic B-mode images to estimate the two-dimensional displacement vector when target tissue is moving, one based on two-dimensional Fourier transformation in a time-space domain. A set of successive ultrasonic B-mode images is acquired from the moving tissue by fixing the ultrasonic probe. A two-dimensional time-space domain image is then synthesized from images thus obtained. Many loci of speckles of high intensity appear in the synthesized image when the tissue moves in the expected direction. Since the inclination of these loci in the time-space domain depends upon tissue displacement, this displacement is derived from the angle of inclination of the loci. Noise in the data is suppressed by deriving this displacement in a Fourier-transformed domain. Agarose gel containing graphite powder was used as a phantom in the basic experiments. In these experiments, an ultrasonic probe was used in conjunction with a linear mechanical scanner, so that a set of B-mode images differing in relative position of the ultrasonic probe in relation to the phantom was acquired. Experiments under the existence of extra movement normal to the B-mode imaging plane were also conducted. Error of estimation in the proposed method was much smaller than that of conventional auto-correlation, especially when actual displacement was smaller than size of the pixels in the original B-mode images.