Motion estimation within an ultrasound image sequence can be performed in several manners. When using block-matching techniques with the maximum likelihood (ML) estimator, one would try to match a block from the first image with a block in the second image, within a predefined search area. The estimated motion vector is the one maximizing a likelihood function, formulated according to the image formation model. Until now, either the classical L1 and L2 norms or a model in which only one image is noisy have been used for motion estimation in ultrasound images. Two new ML motion estimation schemes that are suitable for estimating the motion between noisy ultrasound images are presented. The proposed likelihood functions are based on the assumption that both images contain by a Rayleigh distributed multiplicative noise. Presented experimental results show an improvement in the motion estimation with compared to other known ML motion estimation methods.