From its discovery, crack closure was recognized as a key aspect in understanding the fatigue crack growth process. Considering the condition of plane stress, a vast amount of research has been conducted experimentally, analytically, and numerically to understand the complex process of fatigue crack growth and crack closure. Nonzero crack opening stress values are routinely observed, and it seems that there is a general agreement regarding the incidence of the phenomenon under plane stress. However, investigations regarding crack closure under plane strain conditions are less abundant. Moreover, the existence of crack closure under the plane strain state of the stress has been questioned. The importance of accurate measurements of closure to predict adequately fatigue crack growth rates should not be underestimated. Models employed to predict fatigue crack growth rates rely on plasticity-induced crack closure concepts, and the validity of plasticity-induced crack closure depends on crack closure measurements. Crack closure measurements can be performed with Elber’s Method, the ASTM standard(Compliance offset method), or it may be done alternatively by the compliance ratio (CR) or the adjusted compliance ratio method (ACR). In this research, a small scale yielding two-parameter modified boundary layer analysis is performed to study the occurrence of plasticity-induced fatigue crack closure under constant amplitude loading and plane strain conditions. A wide range of T-stresses and KI levels are considered in the finite element analysis with the purpose of exploring the behavior of the crack opening stress. Crack closure was observed for some values of T-stress. Other values of T-stress resulted in an absence of closure under steady state conditions. In addition, an elastic-plastic finite element model was used to simulate a growing fatigue crack with WARP3D software. The computed displacements were used to determine the effective stress intensity factor range ΔKeff with the ASTM standard compliance offset approach, the (CR) method, and the (ACR) method. Finally, measurement location effects on ACR and the ability of ACR method to remove residuals stresses were investigated.