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Soft tissue needle insertion characterization has been a focus of many medical and biomedical recent studies. In this study the constrained prostate soft tissue deformation through a finite element model is evaluated. The study considers a sensitivity analysis of the target reaching error with respect to the mechanical, insertion and anatomical parameters in presence of the kinematics constraint on the tissue. The needle insertion into the soft tissue is simulated using the proposed Finite Element Method (FEM). Based on acquired results, the insertion of needle induces a considerable rotation of the prostate tissue due to its specific kinematics and support structure. Such rotation can increase the sensitivity of the error to mechanical properties of the tissue especially to the Poisson ratio. It is shown that even minor changes in Poisson ratio (4%) leads to large target reaching errors (9 fold).