Mechanically flexible and conformal shaped electronics is gaining momentum in today's electronics ecosystem. Rapid progress at device and circuit levels are already underway, but researchers are yet to envision the system design in a flexible form. This paper introduces hybrid flexible systems, and coins the term System-on-Polymer (SoP) to combine the advantages of flexible electronics and traditional silicon technology. First, we formally define flexibility as a new design metric in addition to existing power, performance, and area metrics. Then, we present a novel optimization approach to place rigid components on to a flexible substrate while minimizing the loss in flexibility. We show that intuitive placement leads to as much as 5.7x loss in flexibility compared to the optimal placement. Finally, we discuss major challenges in the architecture and design of SoPs.