This paper presents a model of needle tissue interaction forces that a rigid suture needle experiences during surgical suturing. The needle-tissue interaction forces are modeled as the sum of lumped parameters. The model has three main components; friction, tissue compression, and cutting forces. The tissue compression force uses the area that the needle sweeps out during a suture to estimate both the force magnitude and force direction. The area that the needle sweeps out is a direct result of driving the needle in a way that does not follow the natural curve of the needle. The friction force is approximated as a static friction force along the shaft of the needle. The cutting force acts only on the needle tip. The resulting force and torque model is experimentally validated using a tissue phantom. These results indicate that the proposed lumped parameter model is capable of accurately modeling the forces experienced during a suture.