The execution of robotic tasks in dynamic, unstructured environments requires the generation of motion plans that respect global constraints imposed by the task while avoiding collisions with stationary, moving, and unforeseen obstacles. This paper presents the elastic strip framework, which addresses this problem by integrating global motion planning methods with a reactive motion execution approach. To maintain a collision-free trajectory, a given motion plan is incrementally modified to reflect changes in the environment. This modification can be performed without suspending task behavior. The elastic strip framework is computationally efficient and can be applied to robots with many degrees of freedom. The paper also presents experimental results obtained by the implementation of this framework on the the Stanford Mobile Manipulator.