The interaction between the needle and the soft tissue during medical procedures can damage tissue, hindering performance. Reducing tissue damage can improve target accuracy in some procedures, such as biopsies, electrode placement, or drug delivery. This research aims to study the effect of needle speed on tissue damage. For this purpose, we propose a damage model that incorporates the dynamic needle tissue interaction and the plane strain problem related to the hole left in the tissue after needle extraction. The optimization of the model provides a speed which minimizes tissue damage. A hypodermic needle was inserted into ex vivo turkey breast tissue at different insertion speeds. The size of the tissue hole and the friction stress from the needle-tissue interaction were used to measure damage and develop the damage model. The results revealed significant differences in the hole sizes and the friction stress measurements when different insertion speeds were used. Finally, the damage model was fitted to the experimental data and a speed value that minimizes tissue damage could be obtained.