Several mathematical rules by which bone adapts to mechanical loading have been proposed. Previous work focused mainly on negative feedback models, e.g., bone adapts to increased loading after a minimum strain effective (MES) threshold has been reached. The MES algorithm has numerous caveats, so we propose a different model, according to which bone adapts to changes in its mechanical environment based on the principle of cellular accommodation. With the new algorithm we presume that strain history is integrated into cellular memory so that the reference state for adaptation is constantly changing. To test this algorithm, an experiment was performed in which the ulnae of Sprague–Dawley rats were loaded in axial compression. The animals received loading for 15 weeks with progressively decreasing loads, increasing loads, or a constant load. The results showed the largest increases in geometry in the decreasing load group, followed by the constant load group. Bone formation rates (BFRs) were significantly greater in the decreasing load group during the first 2 weeks of the study as compared to all other groups (P < 0.05). After the first few weeks of mechanical loading, the BFR in the loaded ulnae returned to the values of the nonloaded ulnae. These experimental results closely fit the predicted results of the cellular accommodation algorithm. After the initial weeks of loading, bone stopped responding so the degree of adaptation was proportional to the initial peak load magnitude.