A mechanobiological model of bone growth aimed for the design of medical devices for the treatment of limb deformities during childhood and adolescence was developed. Dimensional analysis was introduced as a tool for the systematic evaluation of the influence attributed to different factors that might modify the bone growth process. Simplifications were proposed, allowing the reduction of bone growth relevant parameters to four non-dimensional numbers, representing the chondrocyte sensitivity to stress, the epiphyseal plate geometry, the bone rigidity and the time. Benchmark situations considered for model validation were bone growth under normal conditions and an epiphyseal stapling treatment. A finite elements approach was used to analyze bone growth in the distal portion of the femur. Results are shown to be consistent with corresponding clinical data published in the literature, which indicates the potential of the here proposed method for the design of specific devices and treatments.