Acoustic attenuation represents the energy loss of the propagating wave through biological tissues and plays a significant role in both therapeutic and diagnostic ultrasound applications. Estimation of acoustic attenuation remains challenging but critical for tissue characterization. In this study, an attenuation estimation approach was developed using the radiation-force-based method of harmonic motion imaging (HMI). 2D tissue displacement maps were acquired by moving the transducer in a raster-scan format. A linear regression model was applied on the logarithm of the HMI displacements at different depths in order to estimate the acoustic attenuation. Commercially available phantoms with known attenuations (n = 5) and in vitro canine livers (n = 3) were tested, as well as HIFU lesions in in vitro canine livers (n = 5). Results demonstrated that attenuations obtained from the phantoms showed a good correlation (R² = 0.976) with the independently obtained values reported by the manufacturer with an estimation error (compared to the values independently measured) varying within the range of 15-35%. The estimated attenuation in the in vitro canine livers was equal to 0.32 ± 0.03 dB cm(-1) MHz(-1), which is in good agreement with the existing literature. The attenuation in HIFU lesions was found to be higher (0.58 ± 0.06 dB cm(-1) MHz(-1)) than that in normal tissues, also in agreement with the results from previous publications. Future potential applications of the proposed method include estimation of attenuation in pathological tissues before and after thermal ablation.