A viscous mechanism for the absorption of ultrasonic energy in tissue is considered. It is shown that the viscous forces acting between a suitably chosen distribution of suspended particles or structure elements and a suspending liquid can account for the experimentally observed linear relations between acoustic absorption coefficient and ultrasonic frequency. The frequency band over which linearity obtains is determined by the limits of the distribution of values for the parameters which describe the structure elements. Below the linear range the relation becomes quadratic, in agreement with experiment, and at “high” frequencies a limiting value is approached asymptotically.