The present demand in the development of tunable devices and meta-materials require better understanding of the composite systems. Ferroelectric based composites with solubility or impurities doped interstitially satisfied the specific condition necessary for applications of e.g. frequency, bias, temperature, etc. On the other hand, many composite materials using coupling phenomena have been reported to have their effective properties surpassing the natural materials. The improvement of the properties of composite materials lies on the better understanding of their coupling effects. Conventional science tries to derive theories based on observation and materials characterizations. Taken advantage of the rapid growing computer technology, one used to say "impossible to be measured" or "impossible to see" can now be virtually characterized and visualized by simulation models. In this thesis, computer models of dielectric properties, piezoelectricity, magnetostriction and magnetoelectricity were constructed and verified. And subsequently the materials of interest were simulated and discussed. First, a three dimensional finite element model on dielectric properties of two phases or materials mixture was constructed. The effective permittivity and tan(delta) of Ba0.5Sr0.5 TiO3:MgO composite were simulated and compared with the experimental results. Structural design parameters concepts such as layers stacking, geometry effect, and effect of size of inclusion were visualized and then discussed. Subsequently, dielectric properties of Ba0.5Sr0.5TiO 3:MgO composite were examined changing their volume fraction using Monte Carlo simulation. The type of connectivity of the Ba0.5Sr 0.5TiO3:MgO composite was also discussed. On the other hand, finite element method with Monte Carlo simulation was conducted for the composition (x)Pb0.2Sr0.8TiO3:(1-x)MgO from x=0 to 1 in the paraelectric phase (from -50°C to 200°C), and the results were computed and compared with the experimental data. The temperature dependence of the relative permittivity of composites was well predicted up to 35.5% volume fraction of (Sr0.8Pb0.2)TiO3, which is sufficient for the composition of interest (usually a few percent of MgO). The simulation results showed little discrepancy as MgO volume fraction increases. Several possible factors resulting in the differences between experimental results and simulations were discussed. The empirically estimated critical volume fraction fc proposed by Wakino et al. for Pb0.2Sr 0.8TiO3:MgO composites was here estimated at ∼0.9 throughout the Pb0.2Sr0.8TiO3 paraelectric phase temperature range. The results indicated that the critical volume fraction fc is a system varying parameter. In the final part of the thesis, a magnetostrictive and piezoelectric coupling model that estimates the electric/magnetic transfer efficiency (dE/dH) was presented. The magnetoelectric model was constructed based on two simulation models i.e. piezoelectric model and magnetostriction model. The piezoelectric model was constructed in dielectric model template adding the third rank piezoelectric effect. A commercial PZT transducer was experimentally measured with its properties. Related properties were then input for simulations and the resonance frequency of the specific PZT was successfully predicted. In addition, modes of resonance frequencies of the specific PZT were able to be visualized and identified. The magnetostriction model was constituted with its forth rank property. Mathematical formula and a modified model based on Langevin theory were appended to the original piezoelectric and magnetostrictive equations to simulate the saturated elastic responses in the coupled systems. A laminated Terfenol-D/PZT/Terfenol-D magnetoelectric composite system was modeled that permits simulated evaluation of coupling properties e.g., magnetostrictive coefficient and strain vs. magnetic field response. The electromagnetic transfer efficiency of the modeled results was in good agreement with experimental value in literature. Magnetostrictive response of the specific Terfenol-D was discussed regarding to the rotation of its crystallographic orientation. The results indicated that improvements can be achieved by a proper rotation of the materials orientation.