This paper investigates numerically characteristics of the fluid flow in spatially correlated variable-aperture fractures under effective normal stress conditions. Spatially correlated aperture distributions are generated by using the geostaistical method (i.e. Turning Bands algorithm). In order to represent a nonlinear relationship between the effective normal stress and the fracture aperture, a simple mechanical formula is combined with a local flow model. Obtained numerical results indicate that the fluid flow is significantly affected by the geometry of aperture distribution varying according to the applied effective normal stress as well as the spatial correlation length of aperture distribution. Moreover, by using results simulated in this study, the modified Louis formula representing the relationship between the effective normal stress and the effective permeability of fracture is proposed.