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In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, we adopt two different formulations of the governing equations of motion: a quasistatic formulation that effectively describes smooth deformations, and a fully dynamic formulation that captures large changes in the sheet’s velocity. The former is a differential-algebraic system solved implicitly, while the latter is a purely differential system solved explicitly, using a hybrid integration scheme that adaptively alternates between the two representations. We demonstrate the capacity of this method to effectively simulate a variety of crumpling phenomena. Finally, we show that statistical properties, notably the accumulation of creases under repeated loading, as well as the area distribution of facets, are consistent with experimental observations. Keywords: Crumpling, Differential-algebraic systems, Elastoplasticity