When reinforced concrete (RC) buildings are seismically retrofitted, new members are attached to existing members through interfaces with roughened surfaces using vibratory hammer and post-installed dowel bars. To attach extended members to the outside of an existing frame, the interfaces are subjected to bending moments and shear forces. In other words, interfaces are subjected to the compressive or tensile normal stresses in addition to shear stresses. However, the previous literature is limited in its investigation of the behaviors under such combined stresses. Therefore, in the authors' previous study, the shear strength estimation of the interfaces was proposed; and then, the cyclic model was presented. Although the proposed model can be applied to the interfaces subjected to tensile and shear stresses, the behavior under compressive normal stress was not discussed. Hence, in this study, the model was improved to estimate the cyclic behavior under the different normal stresses. The Saenz model, which is a constitutive law of concrete, was used to evaluate the envelope behavior. In addition, the peak stress was calculated by using the proposed estimation. For the compressive normal stress, the envelope model and peak stress were modified. Subsequently, the proposed cyclic rules were applied; and, a previous dowel model was incorporated into the modified model. The concrete compressive strength was set to 20-23 N/mm 2 , the diameters of the anchor bar were 13, 16, and 19 mm, the compressive normal stress was set to -0.48 N/mm 2 , and the tensile ratio rN was set to 0.00, 0.33, and 0.66. Epoxy adhesive was used. As a result, the modified model agreed well with the test results; the average ratio of the test results to the model results was 0.91-1.12. In addition, with the increase of δ, the effect of the dowel bar was intensified; whereas, under the compressive normal stress, it became insignificant. Finally, it was concluded that the modified model could reasonably estimate the behavior under the various stresses.