Systematic experimental investigation was carried out to examine the phenomena of crack initiation under pure compression fatigue condition with samples having different pre-prepared notches. Finite element analysis (FEA) simulation was also conducted to determine the stress concentration and stress distribution for the tested samples. Although a smooth bar tested under the pure compression fatigue condition with a peak compressive load equal to the yield strength did not show any crack formation, crack was indeed detected under compressive fatigue load in those samples whereby a critical stress concentration was reached. Such critical condition may be expressed through a critical von Mises stress level. In addition, experimental observation indicates that such crack initiation process was indeed always associated with localized plastic deformation