Learning 3D parametric shape models of objects has gained popularity in vision and graphics and has showed broad utility in 3D reconstruction, generation, understanding, and simulation. While powerful models exist for humans and animals, equally expressive approaches for modeling plants are lacking. In this work, we present Demeter, a data-driven parametric model that encodes key factors of a plant morphology, including topology, shape, articulation, and deformation into a compact learned representation. Unlike previous parametric models, Demeter handles varying shape topology across various species and models three sources of shape variation: articulation, subcomponent shape variation, and non-rigid deformation. To advance crop plant modeling, we collected a large-scale, ground-truthed dataset from a soybean farm as a testbed. Experiments show that Demeter effectively synthesizes shapes, reconstructs structures, and simulates biophysical processes. Code and data will be open-sourced.