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The techniques used to estimate axial elastogram usually present a trade-off between elastogram resolution and noise level. It is advantageous to format a series of elastograms of various resolutions because each can provide different information about tissue stiffness. This goal is traditionally achieved by generating displacement fields using various window lengths, which increases computation load significantly. In this study, we achieve the same goal by using a multiresolution strain computation method based on Savitzky-Golay digital differentiators of different lengths, which requires calculating the displacement field only once. Simulation and experimental results show that the elastograms estimated by the proposed method are comparable to those estimated by traditional methods in terms of resolution, elastographic signal-to-noise ratio, and elastographic contrast-to-noise ratio, but the proposed method requires significantly less computational time.