Soft robots demonstrate superior flexibility and maneuverability than traditional rigid robots in many emerging applications. However, it is challenging to have a general modeling and control methodology to deal with soft body dynamics and its interactions with environment. We present a spline-based modeling and control framework for soft robotic systems. The dynamic model is built on non-uniform rational Bsplines (NURBS) that captures material and physical properties of soft body, while preserving exact geometric dynamics with environmental interactions. Using the NURBS-based dynamic model, the robotic optimal control based on general predictive control is designed through coordination among the finite number of control points. Therefore, the infinite-dimensional motion of soft body can be realized by significantly reduced finite particle motion control. We demonstrate the performance of the modeling and motion control framework using the snakeinspired robot simulations and experiments.