Organ growth and adaptation are governed by genetic blueprints and a synergistic interplay between mechanical loading and biochemical signalling. Bone modelling serves as a paradigm for this process, where bone optimizes its morphology in response to environmental demands. The stresses and strains governing bone adaptation can be determined using the Finite Element (FE) Method; however, as the stresses are highly dependent on the bone’s morphology and dimensions, it is essential to account for the gradual process of bone modelling. The bone modelling algorithm presented in this work, implemented in an FE code, calculates volume changes in external elements in response to mechanical demands. The algorithm then computes the nodal displacements that best approximate these volume changes in a least-squares sense via the Moore-Penrose pseudoinverse. Finally, the remeshing technique proposed by Garcia et al. (1) is applied to prevent element distortion. We utilized this algorithm to reproduce the experimental results of Sugiyama et al. (2), who investigated the dimensional changes of murine tibiae subjected to dynamic axial loads of 10 N (40 cycles daily) over 14 days. These authors compared the geometry of various sections along the tibia before and after the application of the aforementioned loading. Miller et al. (3) previously proposed a bone adaptation model to predict tibial growth for the same experiments; however, stresses were calculated using beam theory and image analysis to assess the cross-sectional area and the second moment of area. This simplification is bypassed in the present study, as the model is implemented within an FE framework. Our results demonstrate that a precise and gradual characterization of dimensional changes is essential to accurately predict the final bone morphology. However, this necessitates streamlining the simulation of bone modelling through an algorithm such as the one proposed in this study.