We have investigated the rheological behavior of the quadrilateral defect array formed in cholesteric emulsions, which are composed of water, surfactants, and cholesteric liquid crystals. The defect array is spontaneously formed after stopping the shear to the cholesteric emulsions, between glass plates with a homeotropic anchoring surface. In the formation process of the defect array, Newtonian flow behavior was detected immediately after termination of the preshear; however, the shear yield stress appeared and was increasing with rest time, corresponding to the texture change. The maximum yield stress, which is detected in the well-developed defect array, tends to be proportional to the number of point defects, among the samples with different thicknesses. The stress-strain relation shows the elastic response in the low shear strain region, which obeys Hooke's law; therefore we have discussed the pitch dependence of the elastic constant per one point defect in the defect array. We proposed a simple model to estimate the yield stress of the defect array quantitatively, by considering that the shear deformation induces the compression and elongation of the cholesteric helix. The estimated yield values were in approximate agreement with the experimental results, which means that the shear stress propagates in the defect array through the liquid-crystalline order of the cholesteric helix between neighboring point defects separately anchored on upper or lower glass surfaces.