This study explores a novel procedure for obtaining quantitative information on the mechanical properties of the fiber-matrix interface in composite materials. The method, based on lattice discretization of a medium, simulates actual experiments in detail, including fiber breakage, matrix yield and/or cracking, and interface failure. The paper concentrates on two experiments performed commonly, the so-called fragmentation test for metal matrix, and the pushout/pullout test for metal as well as ceramic matrix composites. Based on the documented capability of the method to simulate actual experimental data, reliable values of (homogenized) interface properties can be obtained. In addition, the simulations provide further understanding of the mechanisms involved during the relevant testing. Although this study presents results from basic problems, the method is general enough to include effects of residual stress, of high temperature environment, and of dynamic crack propagation, as well as three-dimensional details of the interface failure process. The potential exists for simulating nondestructive wave-based techniques aimed at evaluating interface properties.