Abstract: Transverse compression of wood is a process that induces large deformations. The process is dominated by elastic and plastic cell wall buckling. This work reports a numerical study of the transverse compression and densification of wood using a large-deformation, elastic–plastic constitutive law. The model is isotropic, formulated within the framework of hyperelasticity, and implemented in explicit material point method (MPM) software. The model was first validated for modeling of cellular materials by compression of an isotropic cellular model specimen. Next, it was used to model compression of wood by first validating use of isotropic, transverse plane properties for tangential compression of hardwood, and then by investigating both tangential and radial compression of softwood. Importantly, the discretization of wood specimens used MPM methods to reproduce accurately the complex morphology of wood anatomy for different species. The simulations have reproduced observations of stress–strain response during wood compression including details of inhomogeneous deformation caused by variations in wood anatomy. © 2014, Springer-Verlag Berlin Heidelberg.