Intravoxel phase dispersion (IVPD) in MRE describes signal loss of the MR magnitude due to spin dephasing imposed by voxel deformation. The extensity of IVPD is, among other parameters, dependent on the tissue stiffness. Therefore, tissue stiffness can be quantified by analyzing IVPD-imposed signal loss within a single voxel. The new approach does not rely on the use of spatial derivative operators as in conventional MR Elastography. In the present work, we examine in simulations the extensity of IVPD for varying experimental conditions and present stiffness maps of an inhomogeneous phantom, which were calculated by numerically fitting the IVPD equation.