Three-dimensional ultrasound imaging systems involve two major difficulties as compared with two-dimensional ones, namely, complexity of the data acquisiton ststem and complexity of interpolation of the acquired data when the image is to be displayed on arbitrary planes. In order to solve both problems simultaneously, I have proposed the use of an annular array for two-dimensional scanning and variable sampling rate in the A/D conversion(instead of fixed sampling rate) so that the sampled data are uniformly distributed on any plane perpendicular to the transducer axis when it is directed to the center of the medium under interrogation. In this way the interpolation needed for three-dinmensional display suffice to be one-dimensional or at most two-dimensional, depending on the choice of the orientation of the image display plane. Ultrasound speckle not only obscures the fine structrue of the B-mode image but also adversely influences further image processings such as spectral estimation and edge detection. Therefore, some means are required to remove or reduce speckle. In order to reduce the speckle, two approaches have been proposed in the past, namely, incoherent processing techniques and post formation image filtering techinques. Recently, a growing interest is focused on the post formation image filtering techniques which are applied to the envelope detected B-mode image and several adaptive techniques have been developed. In this thesis, a new post formation image filtering technique inwhich the size and shape of a seed region is adaptively varied to determine the locally homogeneous region around a given filtering point is developed. To simulate the proposed three-dimensional system and new filtering technique, I have developed a simulator for the two-dimensional linear, sector scan B-mode imaging system of linear and annular array transducer. Several simulation and experimental results are shown.