The purpose of this study is to examine the wave propagation in a fractured medium using numerical models and to quantify their limitations and the range of applicability. This work is motivated by the needs of the industries to understand the physics of fractures and minimise uncertainties with the most efficient methods. The finite difference code WAVE3D has been used to model wave propagation in fractured media. In this thesis I present a brief description of the background theory of the code and the theory of the three approaches for fracture representation; the explicit model, the Effective medium (EM) and the Localised effective medium (LEM). These three models are compared in this work. A laboratory experiment with multiple parallel fractures under controlled conditions has been modelled using the above approaches creating synthetic waveforms. A methodology was first developed to invert the source from the experiment so that it could be applied to the numerical models. The performance of the models is evaluated for both uniform and for non-uniform fracture stiffness based on the background stress field. For the last case a new code has been developed to calculates stress dependent stiffness for the EM and LEM. The stress dependent models are a better approach to real data. Low-pass filter method is used to define the frequency range of applicability for the models. The performance and flexibility of LEM is then examined against explicit and EM models to define the balance between maximum wave frequency, fracture stiffness and model's grid quality. Then I evaluate the performance of the fracture representations in media with complex fractures, using a Distinct Element Method code, and applying the effect of complex fractures to the LEM and EM models. I work on how to implement a dipping fracture of the 3DEC numerical code with tetrahedral elements in the WAVE3D staggered grid by either pixelising the fracture or by using an equivalent discrete fracture medium. Finally, based on the methodology developed earlier, I model a seismic cross-hole tomography survey for the EDZ of the GDF in Finland. Due to the non-controlled environment of the survey, the complexity of the studied area cannot be fully represented to the models, and the waveforms of the models are not expected to fully match the survey data. An optimisation process for fracture stiffness is applied to improve the model data for selected ray paths. I reach a range of conclusions on the performance of the different fracture models, fracture stiffness and the techniques developed.