Virtual reality techniques can be used for the training of needle insertion interventions. Visuo-haptic training environments consist of a visual display of a simulated scene and a force-feedback device for haptic interaction. Here, we address the visualization of deformations of soft tissue in real-time. A finite differences method is used to calculate inverse displacement fields and deform volumetric image data in a liver puncturing scenario. Real patient CT-image data was used for this. A diffusive and linear-elastic formulation of the propagation of deformations in the inverse displacement field is augmented with a material function and a simplified modeling of a needle sliding in tissue. Evaluation has been done by comparison of the resulting inverse displacement from this algorithm to those from a finite element simulation. Based on the patient image data, a 2D mesh for the finite element simulation was created. On several points on the mesh, a needle insertion has been performed. Additionally, computational times of the implemented methods are measured to prove its real-time capability and the benefit of an implementation on general purpose graphics hardware. The results show a slightly better performance of the difusive formulation.