This paper presents an extension of the immersed interface method (IIM) to simulate 2D incompressible viscous flows with non-smooth objects. The IIM uses singular forces to represent the effect of immersed objects on the fluid flow. Previously, the IIM was developed for smooth objects. This work describes how to compute necessary jump conditions using line segment representations of non-smooth 2D objects. Tests on flows past stationary and moving non-smooth objects like squares and a Mustang car model indicate the method achieves second-order accuracy and is robust and efficient for multiple moving complex objects. Ongoing work focuses on parallelizing the method for distributed memory computing.