This article presents a method for measuring three-dimensional mechanical displacement and strain fields using stimulated echo MRI. Additional gradient pulses encode internal displacements in response to an externally applied deformation. By limiting the mechanical transition to the stimulated echo mixing time, a more accurate static displacement measurement is obtained. A three-dimensional elasticity reconstruction within a region of interest having a uniform shear modulus along its boundary is performed by numerically solving discretized elasticity equilibrium equations. Data acquisition, strain measurements and reconstruction were performed using a silicone gel phantom containing an inclusion of known elastic properties. A comparison between two-dimensional and three-dimensional reconstructions from simulated and experimental displacement data shows higher accuracy from the three-dimensional reconstruction. The long-term objective of this work is to provide a method for remotely palpating and elastically quantitating manually inaccessible tissues.