Abstract Elastography is a method for imaging the elastic properties of compliant tissues which produces gray scale elasticity images called elastograms. The elastograms of phantoms with homogeneous elastic properties exhibit a noisy appearance. We demonstrate that this noisy appearance of the elastograms is due to the nonstationary relationship between the pre- and postcompression signals that results in an artifactual modulation of the strain estimates by the amplitude variations of the envelope of the rf signal. We have identified two methods to reduce the strain modulation artifact. The first method consists of reducing the signal amplitude swings within the observation windows by logarithmically or otherwise compressing the rf signal. The sensitivity of this method to amplitude compression strength and the ability to reduce the noise in the elastograms without affecting the spatial resolution are investigated through simulations. The second method to reduce the strain modulation artifact consists of temporal stretching of the signal obtained after physical compression to approximate the shape of the signal obtained before compression. In this paper, we discuss the first method. The results show that significant improvement in image noise can be obtained with logarithmic amplitude compression. This improvement is obtained in conjunction with improved spatial resolution.