A one dimensional creep and stress relaxation response of cancellous bone to instant loading is investigated based on the studies with scanning microscope, can cancellous bone be viewed as a cellar solid consisting of an interconnected skeleton filled with medulla. A two phase poroelastic model is introduced to describe the cancellous bone, in which the tissue(material) densities of the skeleton and medulla are assumed to be unchangeable while the corresponding apparent densities are changeable due to the change of volume fraction. The governing equations are derived for the case of a linear poroelastic solid skeleton saturated with an inviscid medulla. Under the loading, responses of the skeleton stress as well as the medullary pressure are obtained with Laplace transform technique. The computational result shows that the cancellous bone is provided with certain features similar to those appearing in viscoelastic solids, which means the responses do not only depend on time, but furthermore depend on previous loading history. It is worth paying attention to the result that the medullary pressure can be negative. This point is due to the recovery of the skeleton after unloading whereas the medulla is not squeezed out but absorbed into the pores by suction.