The evaluation of the material properties of masonry built with traditional lime mortar remains largely unclear to what extent the complex mechanical behavior of its constituents and sampling difficulties. This article presents the experimental results of a research project carried out on the four unreinforced masonry (URM) walls with four different types of lime mortars used in the Roman and Byzantine periods under shear-compression. Besides, an elasto-plastic damage (EPD) approach is adapted calibrating the parameters of Oliver's damage model and the modified von-Mises yield criterion for the masonry constituents. For the modeling purposes, a new fictitious joint material approach is introduced to describe the constitutive behavior of both mortar and mortar-brick interface. The proposed approach can be useful to describe the behavior of mortar and mortar-unit interface in existing masonry structures.