Masonry structures, usually being composed of a repeating geometric pattern, lend themselves well to analysis using periodic unit cells. Based on stress and strain equilibriums and rational assumptions concerning the interaction of the components of the cell, one may propose micro-mechanical models using simple analytical expressions which simulate well the behavior of masonry. Models describing the nonlinear behavior of masonry constituent materials may be implemented in such models and used to simulate the failure modes anticipated to arise in the composite. In this way, the nonlinear behavior of masonry composites may be derived, as defined by the interaction of its two main material phas-es: units and mortar. Taking advantage of the low computational cost of models based on analytical expres-sions, which is only a fraction of those based on finite element simulations, wide and in-depth parametric analyses can be performed with ease. In this paper, a model for the nonlinear behavior of masonry is presented and used in a parametric study, investigating the influence of various material properties on its compressive strength. The results indicate a strong dependence of the compressive strength of masonry on material parameters that are difficult to measure accurately or are often ignored, particularly in existing and historic masonry structures.