To date, elastographic imaging techniques such as magnetic resonance elastography (MRE) have primarily been considered isotropic material properties, despite the fact that most biological tissues tend to have some anisotropic qualities. In this thesis, a finite-element based orthotropic, incompressible material model is used as the basis for the in vitro MRE gelatin phantom. This study includes the use of biologically based orthotropic gelatin phantoms, with MRI data acquisition and boundary conditions suitable to describe the orthotropic material behavior. Fabricating a biological gelatin phantom using pineapple for MRE in vitro testing is a novel technique which was developed specially for this study. Multiple motion measurements from the pineapple gelatin phantom were made by applying directionally independent boundary conditions within the 85-125 Hz frequency range. Such multiple, orthogonal excitation data is needed to provide a complete description of the mechanical properties of this anisotropic phantom, given the potential for non-uniqueness of the reconstructed property estimates. Orthotropic image reconstructions were then carried out to map orthotropic elasticity properties in 3-D based on MR detected motion datasets captured from the pineapple gelatin phantom. The subzone based orthotropic incompressible reconstruction algorithm was based on the Conjugate Gradient optimization method, to gain computational efficiency, and used total volitional (TV) regularization techniques to constraint the solution process. The adjoint-residual method was utilized to improve the efficiency of the gradient descent based algorithm. The elasticity image reconstruction results presented for the orthotropic incompressible phantom are also correlated with isotropic property reconstructions for the same phantom.