During minimally invasive surgical procedures (e.g., needle insertion during interventional radiological procedures), needle–tissue interactions and physiological processes cause tissue deformation. Target displacement is caused by soft-tissue deformation, which results in misplacement of the surgical tool (needle). This study presents a technique to predict target displacement in three-dimensions (3D) by combining soft-tissue elasticity estimation using an ultrasound-based acoustic radiation force impulse (ARFI) technique and finite element (FE) models. Three different phantoms with targets are manufactured, and subjected to varying loading and boundary conditions. Ultrasound images are acquired using a 3D probe during loading and unloading of each phantom, and subsequently target displacement is calculated. 3D FE models of the phantoms are developed, and they are used to predict target displacement. The maximum absolute error in target displacement between the experiments and FE analyses is found to be 1.39 mm. This error is less than the smallest tumor diameter (2.0–3.0 mm) which can be detected in breast tissue. This study shows that the combination of soft-tissue elasticity estimation using the ARFI technique and 3D FE models can accurately predict target displacement, and could be used to develop patient-specific plans for surgical interventions.