In order to understand the nature of kink band formation in high performance fibers, the compression behavior of pitch and PAN-based carbon fibers (P75S, T-50, T-300, and GY-70), and of polymeric fibers (DuPont Kevlar; PBZr; and PBO) was measured using a micro-scale compression apparatus in an optical microscope. With increasing compressive strain, kink band formation was observed and the number of kink bands per unit length (referred to as kink band density) was determined. By extrapolating to zero kink band density, the critical compressive strain for rigid-rod polymeric fibers was obtained and compared to that of the carbon fiber. Using the Euler buckling equation, a fundamental dimension of the buckling element for the compression of PBO and PBZT fibers was calculated to be a 0.42-0.57 mum diameter fibril, and not the smaller diameter microfibrils.