This study demonstrates synthesis of seismic responses in general elastic and viscoelastic fractured media using a two-dimensional pseudo-spectral method. From the full waveform simulation approach, different types of source configurations with corresponding wavefields and synthetic records are generated. Viscoelastic wavefield responses, which incorporate quality factors for both P-waves (Qp) and S-waves (Qs) through the superposition of relaxation mechanisms and velocities for attenuative and dispersive media, are presented, tested and implemented to assess their potential for practical application. The modeling results show that the more time that elapses, the less the wave amplitudes can be observed in a viscoelastic media than in elastic media. The simulation of both pressure and shear source fully illustrate the corresponding decomposed waves and their corresponding seismograms. Also, the synthetic model of the anticline structure embedded in the layered model shows that diffraction responses are directly related to the fracture/fault zone structure. From the prescribed model, transmission, reflection, and converted multi-phase events can readily be identified in both elastic and viscoelastic media. Aside from this, evaluating seismic responses using a specially designed source and receiver configuration, such as horizontal drilling technique, is critical in studies pertaining to reservoirs. It is also demonstrated that by examining such seismic responses, the effects of fracture distributions and the corresponding time-lapsed monitoring of oil/gas leakage within a reservoir can be evaluated in advance by the proposed method for numerical studies.