Rock formations often exhibit transversely anisotropic elastic behavior due to their layered structure. Such materials are characterized by five independent elastic constants. In the context of petroleum applications, it is often challenging to accurately measure all these elastic parameters. At the same time, the effect of elastic anisotropy can be noticeable and therefore there is a need to include it in some form. To fill the gap, this study proposes a three parameter elastic anisotropy model. It captures the dominant anisotropic behavior and yet has only three elastic constants that are relatively easy to measure in laboratory. The approach is based on upscaling of a periodically layered material characterized by equal height layers with different Young's moduli and the same Poisson's ratio. The resultant upscaled material is transversely isotropic and is also physically admissible. The developed approach allows to effectively reconstruct or estimate the values of the two remaining parameters needed for the transversely isotropic model. Comparison between the reconstructed results and the measured values are compared for several rock types.