In a long-lived organism with a modular architecture, such as trees, somatic mutations accumulate throughout the long lifespan and result in genetic mosaicism in each module within the same individual. In recent years, next-generation sequencing technology has provided a snapshot of such intra-organismal genetic variability. However, the dynamic processes underlying the accumulation and expansion of somatic mutations during the growth remain poorly understood. In this study, we constructed a model to describe these processes in a form that can be applied to a real tree. Given that the proliferation dynamics of meristematic cells vary across plant species, multiple possible processes for elongation and branching were comprehensively expressed in our model. Using published data from a poplar tree, we compared the prediction of the models with the observation and explained the cell lineage dynamics underlying somatic mutations accumulation that were not evident from the snapshot of the sequenced data. We showed that the somatic genetic drift during growth increases inter-meristem mosaicism, resulting in genetically distinct branches and less integrity within an individual tree. We also showed that the somatic genetic drift during branching leads to the mutation accumulation pattern that does not reflect the tree topology. Our modelling framework can help interpret and provide further insights into the empirical findings of genetic mosaicism in long-lived trees.