Precise insertion of a medical needle as an end-effecter of a robotic or computer-aided system into biological tissue is an important issue and should be considered in different operations, such as brain biopsy, prostate brachytherapy, and percutaneous therapies. Proper understanding of the whole procedure leads to a better performance by an operator or system. In this chapter, the authors use a 0.98 mm diameter needle with a real-time recording of force, displacement, and velocity of needle through biological tissue during in-vitro insertions. Using constant velocity experiments from 5 mm/min up to 300 mm/min, the data set for the force-displacement graph of insertion was gathered. Tissue deformation with a small puncture and a constant velocity penetration are the two first phases in the needle insertion process. Direct effects of different parameters and their correlations during the process is being modeled using a polynomial neural network. The authors develop different networks in 2nd and 3rd order to model the two first phases of insertion separately. Modeling accuracies were 98% and 86% in phase 1 and 2, respectively.