The effect of losses in the dissipative object becomes crucial when maximal power absorption of the incident wave is of top priority. In order to assess the phenomenon of acoustic power absorption in finite size dissipative medium, a prototype model of linear pressure waves absorption in dissipative layer is considered. The conditions, parameters and bounds for the optimal (maximal) incident power absorption within the layer have been found analytically and explicitly versus its normalized thickness. These conditions are presented in terms of the basic wave propagation parameters, namely sound velocity and attenuation constant. It is shown that, for thin layers (in terms of acoustic wavelength), the upper bound on the absorptivity tends to the value of 50%, when prescribed resonant dispersion/absorption conditions, characterized by the so-called Kramers–Kronig relations, are met within the layer. For sufficiently thick layers absorption of close to 100% of the incident wave power can be achieved, when specific optimal values are selected for the corresponding real and imaginary parts of dissipative layer wave number. The model may serve as a canonical prototype problem for engineered dissipative materials design and optimization of the sound/ultrasound absorption in lossy targets, e.g., biological tissues. © 2004 Acoustical Society of America.