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The mechanical response of p-phenylene terephthalamide (PPTA) single fibers when subjected to uniaxial compression is investigated computationally using coarse-grained molecular statics/dynamics methods. In order to construct the coarse-grained PPTA model (specifically, in order to define the nature of the coarse-grained particles/beads and to parameterize various components of the bead/bead force-field functions), the results of an all-atom molecular-level computational investigation are used. In addition, the microstructure/topology of the fiber core, consisting of a number of coaxial crystalline fibrils, is taken into account. Also, following our prior work, various PPTA crystallographic/topological defects are introduced into the model (at concentrations consistent with the prototypical PPTA synthesis/processing conditions). The analysis carried out clearly revealed (a) formation of the kink bands during axial compression; (b) the role of defects in promoting the formation of kink bands; (c) the stimulating effects of some defects on the fiber-fibrillation process; and (d) the detrimental effect of the prior compression, associated with fiber fibrillation, on the residual longitudinal-tensile strength of the PPTA fibers.