Objective To investigate the stress relaxation response of bony tissue under constant displacement loading. Methods A modern porous medium model was developed to do the research on the mechanical behavior of fluid saturated living bone tissue based on the mixture theory by using the Laplace transform technique. Results A one dimensional governing equation is derived for the case of a linear poroelastic solid skeleton saturated with viscid bony fluid. The result shows that the bone tissue is provided with certain features similar to those appearing in viscoelastic solids, which means the responses do not only depend on time, but also depend on previous loading history. Conclusion Viscoelastic behavior and energy dissipation of cancellous bone are depended on the flow and diffusion rate of the fluid composition in bone.