In many rock types, such as shales, elastic parameters vary with propagation directions, defined as elastic anisotropy. Recent advances in seismic data acquisition requires the need to include anisotropy information for imaging and processing. However, anisotropy model building is not straightforward due to data availability. Here we present a multi-objective approach to find an optimal solution using both well logs and seismic data. We use seismic objective as a constraint to narrow the uncertainty distribution around model parameters and to ensure that the model is consistent with seismic as well as well log data. Consequently, the resulting anisotropy model can be used for both well logs and seismic data analysis. First, Hudson-Cheng crack model is used to obtain rock matrices properties (bulk and shear moduli) and aspect ratio of a set of ellipsoidal cracks. Then, we obtain a set of non-dominated solutions, which minimizes the RPM (rock-physics model) multi-parameter objective function and the AVO (Amplitude Versus-Offset) objective function. The approach is applied to a field data with one vertical well log and pre-stack migrated seismic data. In spite of the low signal-to-noise ratio of seismic data, the overall results are consistent with the rock-physics model and fit the seismic amplitude variations, particularly for the mid-to-far angles of incidence. Furthermore, we extend the approach to predict seismic anisotropy away from well log location, to map the occurrence of high quality organic-rich shales.