Remodeling is a critical feature of living tissue such as bone tissue. From the mechanical viewpoint, it is recognized as a regulation process of stress due to tissue growth and atrophy. The volumetric change of the bone tissue causes the nonuniform natural state, and because of the statical indeterminacy, the residual stress may remain in the tissue even when all external forces are removed. Permitting the existence of the residual stress, a rate-type model is proposed for the mechanical bone remodeling by means of volumetric growth/atrophy of the tissue. The rate of remodeling is expressed as a function of the local stress and its derivatives, seeking the equi-stress state. This does not refer to any goal stress specified a priori. The basic features of the proposed model are examined by using a simple model of diaphysial bone. The case study is conducted for the simplified tibia-fibula system, and it is demonstrated that the proposed model has the capability to describe the bone remodeling process qualitatively.