Earthquakes are one of the most significant destructing natural hazards affecting a large population worldwide. For this reason, ground motion predictions are critical to evaluate the seismic hazard in highly populated areas, which in some cases, are located on site conditions prone to seismic amplification. Soil amplification is one of the most important factors affecting the earthquake ground motion. When the incident wave field is strong enough and the soil strength is relatively weak, nonlinear material behavior appears, introducing important changes such as soil degradation, and if the material is granular and water saturated, cyclic mobility and liquefaction. In this work, I study the numerical modeling of wave propagation in 1D/2D complex media that include nonlinear soil behavior under the framework of the spectral element method (SEM). The consideration of soil nonlinearity holds an important place in order to achieve simulations consistent with real observations for strong seismic shaking. Additionally, in the presence of strong ground motion in saturated soils, pore pressure becomes an important parameter to take into account for related phenomena such as flow liquefaction and cyclic mobility. In this study, first, one component (1C) - seismic wave propagation is modeled in linear and nonlinear media in 1D based on the spectral element numerical method. Viscoelastic and nonlinear soil rheologies are implemented by use of the memory variables technique and Iwan’s elastoplastic model, respectively. Then, the same study is extended to a 1D - three component (3C) model and a preliminary comparison on the effect of using 1C and 3C approaches is made. Then, the influence of excess pore pressure development is included in the 1D-3C model and the developed numerical model is applied to realistic case on the site of Wildlife Refuge Liquefaction Array (USA) which is affected by the 1987 Superstition Hills event. The ground motion modification for different assumptions of the soil rheology in the media and different input motions is studied. The calculated motion is found to be amplified on low frequency and damped in high frequency range due to excess pore pressure development. Furthermore, the soil is found to be more nonlinear under triaxial loading in 3C approach and more dilatant due to higher nonlinearity. Despite the similitude in surface acceleration and velocity results, significant differences in surface displacement results of 1C and 3C approaches are remarked. Similar analyses are performed on two Japanese sites Kushiro Port and Onahama Port, which are influenced by the 1993 Kushiro-Oki and the 2011 off the Pacific coast of Tohoku earthquakes, respectively. It has been shown that the nonlinearity-related changes are not homogeneous all over the concerned frequency band and the influence of cohesionless soil behavior on wave propagation is highly dependent on model properties and loading conditions. Lastly, the 2D SEM code is developed by taking into account soil nonlinearity and pore pressure effects similarly to 1D-3C SEM code. The developed 2D SEM code is applied to a 2D sedimentary basin site where the basin geometry is asymmetrical and soil profile consists of layers with different nonlinearity properties. P-SV and SH 2D wave propagation considering dry (total stress) and saturated (effective stress) soil conditions are performed. The calculated surface motion differs significantly as a function of the input motion loading conditions and the resultant deformation in superficial layers can be very high in effective stress analysis compared to total stress analysis. Furthermore, material nonlinearity is traduced by a reduction of the seismic wave speed making wave propagation takes longer time inside basin media and the reflections on bedrock-basin boundaries lead the soil in basin edges to higher nonlinearity. This study shows the possibility of modeling nonlinear soil behavior including pore pressure effects in seismic wave propagation studies by coupling different models with spectral element method. These analyses help identifying and understanding dominant phenomena occurring in superficial layers, depending on local conditions and input motions. This is of great importance for site-specific studies.