Though motion planning has been studied extensively for rigid and articulated robots, motion planning for deformable objects is an area that has received far less attention. In this paper we present a framework for planning paths in completely deformable, elastic environments. In particular we apply a deformable model to the robot and obstacles in the environment and we present a kinodynamic planning algorithm suited for this type of deformable motion planning. The planning algorithm is based on the Rapidly-Exploring Random Tree (RRT) path planning algorithm. To the best of our knowledge, this is the first work that plans paths in totally deformable environments.