MPeat2D is a fully coupled mechanical, ecological, and hydrological model of long-term peatland growth in two dimensions, which takes spatial variability and structure into consideration. MPeat2D is developed based on poroelasticity that couples fluid flow and solid deformation. The formulation of MPeat2D is divided into mechanical, ecological, and hydrological submodels. This software is the supplementary material for journal published in the Earth Surface Dynamics with the title 'MPeat2D-A fully coupled mechanical-ecohydrological model of peatland development in two dimensions'. MPeat2D is the extension of the earlier one-dimensional mechanical-ecohydrological model of peatland growth, called MPeat, that has been published in the Mahdiyasa, A. W., Large, D. J., Muljadi, B. P., Icardi, M., & Triantafyllou, S. (2022). MPeat—A fully coupled mechanical-ecohydrological model of peatland development. Ecohydrology, 15(1), e2361. https://doi.org/10.1002/eco.2361 Mahdiyasa, A. W., Large, D. J., Muljadi, B. P., & Icardi, M. (2023). Modelling the influence of mechanical-ecohydrological feedback on the nonlinear dynamics of peatlands. Ecological Modelling, 478, 110299. https://doi.org/10.1016/j.ecolmodel.2023.110299