Finite element simulation of contact/impact problems using the penalty method is a well-established capability. The automatic penalty stiffness provides an easy way to implement the contact analysis. However, this way in which the penalty stiffness is associated with the material property and geometry of the master surface can lead to inappropriate distributions of contact pressure at edges or mesh transitions, or even cause much numerical noise. A new method of defining the penalty stiffness, which is associated with geometry of the slave surface, the reference penetration and reference contact pressure, is developed to consistently relate forces on contacting nodes with the contact pressure. This technique is successfully applied to several examples as the clamping simulation during the punch test and the rolling process. The results of such applications of new contact stiffness model demonstrate the effectiveness of such a model in avoiding the stress edge effect and the accompanying numerical noise. As an alternative approach to define the penalty stiffness, this new model provides another option for the contact analysis and gives the users more possibilities to control the contact performance. / Thesis / Master of Engineering (ME)