Porous rocks, subjected to compressive stress, often undergo mechanical compaction via grain crushing and grain rearrangement, and chemical compaction by pressure solution. Such volume reduction processes are known to spontaneously localize under certain conditions, creating compaction and compacting shear bands, solution seams, and stylolites. However, the localization process is poorly understood. The formation and propagation of compaction bands have recently been studied using an elastoplastic spring network model (Katsman et al., 2005). In this paper, the same technique was employed to systematically analyze localized volume reduction (LVR) defects and their interactions with the surrounding elastic media, i.e., the stress distribution around an LVR region. Simulation results show that LVR regions experience stress concentrations at their tips, reminiscent of mode I cracks. However, aside from this similarity point, comparison of stress around LVR regions to stress around cracks reveals that the stress/strain distribution in such LVR defects is quite different than that surrounding mode I cracks. Implications for stylolites and compaction band are thoroughly discussed.