The importance of simulation in engineering research is undeniable, the fact that its application needs much less money than physical tests reduces research and development costs drastically. The present thesis deals with the development and implementation of a constitutive model of different anisotropic, viscoelastic material behaviour for carrying out steady state dynamics simulations. The types of anisotropy studied are concretely cubic anisotropy and orthotropy, which can be easily simplified to transversal isotropy. For achieving this objective, the most important theoretical concepts are developed, ranging from elasticity and linear viscoelasticity theories to some Finite Element Method techniques. The constitutive model will be programmed in an Abaqus UMAT subroutine. This UMAT allows the implementation of the material constitutive law in Abaqus commercial software to carry out the desired frequency domain studies, or, more precisely, to predict how the material behaves under the effect of harmonic excitaton. The material input data for the UMAT is obtained through simulations applied to unit cells with the structure and material properties under study. By these unit cell and with periodic boundary conditions, an infinitely repeating pattern of the cellular architecture is simulated. Furthermore, the quality of the UMAT predictions will be intensely tested through different simulations at different frequencies. Such simulations will be applied to both the inhomogeneous unit cell and an homogenous unit cell whith the homogeneized input data applied through the UMAT. The results from both simulations will be compared in order to test the accuracy of the simulations when the UMAT is applied. Some UMAT applications are also dealt. On one side, the UMAT for cubic anisotropy will be applied to a cubic finite model with different material principal directions. On the other hand, a DMA model is developed and implemented to simulate a four-layered composite with different configurations in the transversally isotropic layer orientations.