Extra-corporeal membrane oxygenation (ECMO) is a procedure that allows the circulation and direct oxygenation of blood in the event of lung injury or dysfunction. ECMO requires a team of trained medical professionals which creates a burden to persons in need such as injured soldiers on the battlefield or those suffering from a pandemic in which medical staff is already stretched thin. This thesis explores the initial step of automating ECMO which is force modeling of needle insertion into jugular or femoral blood vessels. A comprehensive force model consisting of stiffness, cutting, and friction forces was created that accounts for each phase of needle insertion through multiple layers. This model is simulated and then adjusted to empirical results from porcine and bovine samples. This thesis presents a unique force model for a specific target location with multiple layers, as well as takes into account tissue deformation recovery which is an under-researched phenomenon. This reasonable lumped parameter model allows for the application of a control law.