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Experimental results have shown that in the megahertz frequency range the relationship between the acoustic attenuation coefficient in soft tissues and frequency is nearly linear. The classical continuum mechanics (CCM),which assumes that the material is uniform and continuous, fails to explain this relationship particularly in the high megahertz range. Doublet mechanics (DM) is a new elastic theory which takes the discrete nature of material into account. The current DM theory however does not consider the loss. We revise the doublet mechanics (DM)theory by including the loss term, and calculate the attenuation of a soft tissue as a function of frequency using the modified the DM theory (MDM). The MDM can now well explain the nearly linear relationship between the acoustic attenuation coefficient in soft tissues and frequency.