We present here a short summary of two rather different, but complementary, simulations of plastic deformation in a flexible chain glassy polymer. In the first, atomistic simulation, a molecular structure model is used in which well‐established force fields between atoms and atom groups on a typical chain polymer are introduced to account for the most relevant molecular degrees of freedom that govern both structural and shear relaxations. The principal result of this simulation which has been described in great detail elsewhere [Mottetal., Philos. Mag.67, 931–978 (1993a)] is that shear relaxations are in the form of abrupt shear transformations occurring in volume elements of ∼10 nm size and resulting in transformation shear strains of ∼2%. This simulation has established that the chemically specific conformational constraints are internal to the volume elements and that the interaction of the elements with their surroundings is elastic, suggesting that the phenomenon can be meaningfully simulated by a two‐dimensional mesoscopic model. In the second part of the present communication we summarize the most important findings of the extensive two‐dimensional mesoscopic simulation which we [Bulatov and Argon, Model. Sim. Mater. Sci. Eng.2, 167–184 (1994a); 185–202 (1994b); 203–222 (1994c)] have performed. These findings include the important effects of disorder related misfit stresses in governing both quasihomogeneous flow at elevated temperatures and localized shear flow at lower temperatures. In addition, we demonstrate that these misfit stresses are the key ingredient that governs the initial deformation transients, as well as the well‐known distributed kinetics of the deformation process in amorphous media in general.