Convection-enhanced delivery (CED) is a technique to bypass the blood-brain barrier and deliver therapeutic agents into the brain. However, animal studies and preliminary clinical trials have reported reduced efficacy to transport drugs in specific regions, attributed mainly to backflow, in which an annular zone is formed outside the catheter and the fluid preferentially flows toward the surface of the brain rather than through the tissue toward the targeted area. In this study, a finite element model of backflow was updated by implementing the pre-stress generated during needle insertion, which allows considering the effect of needle insertion velocity during CED infusions in agarose gel. The nonlinear mechanical properties of the agarose solutions were obtained by fitting experimental data from stress-relaxation tests. Additional experimental measurements of backflow lengths were used to adjust the pre-stress model. The developed model was able to reproduce changes of backflow length under different insertions velocities and flow rates. These findings reveal the relevance of considering the pre-stress in the tissue located around the needle surface during CED infusions into the brain.