Microtubules play a crucial role in dendritic and axonal physiology through acting as railroad tracks on which numerous factors are transported. More than one hundred microtubules in a neurite form a large array that changes in composition during the development of dendrites and the axon. Throughout development, this large array was long thought to act as the stationary backbone of neurons. In contrast, we recently made the surprising discovery that the microtubule array in fact constantly moves towards the soma as a whole. This microtubule retrograde flow (MT-RF) destabilizes neurite growth. Through slowing down in the axon but staying active in other neurites, MT-RF determines which neurite will become the axon and which neurites will develop into dendrites. To investigate how the new perspective that MT-RF provides affects developmental changes of the MT array, we developed a mathematical model. This model includes several mechanisms acting on microtubules, particularly MT-RF and microtubule stabilization. Since there was no model of the neuronal microtubule array to build upon, we identified mechanisms to include in the model by comparing models with different sets of mechanisms to experimental data we acquired. Among other things, the model provides insights into how stable microtubules accumulate in neurons, which is an important process in neuronal development. Of note, the model suggests that MT-RF reduces the accumulation of stabilized microtubules. This new model lays an important foundation to quantitatively understand developmental changes of the microtubule array in dendrites and the axon.