3D registration of ultrasound images is an important and fast-growing research area with various medical applications, such as image-guided radiotherapy and surgery. However, this registration process is extremely challenging due to the deformation of soft tissue and the existence of speckles in these images. This paper presents a novel intra-modality elastic registration technique for 3D ultrasound images. It uses the general concept of attribute vectors to find the corresponding voxels in the fixed and moving images. The method does not require any pre-segmentation and does not employ any numerical optimization procedure. Therefore, the computational requirements are very low and it has the potential to be used for real-time applications. The technique is implemented and tested for 3D ultrasound images of liver, captured by a 3D ultrasound transducer. The results show that the method is sufficiently accurate and robust and does not easily get trapped with local minima.