Continuum manipulators, featuring “continuous backbone structures”, are promising for deft manipulation of a wide range of objects under uncertain conditions in less-structured and cluttered environments. A multi-section trunk/tentacle robot is such a continuum manipulator. With a continuum robot, manipulation means a continuous whole arm motion, where the arm is often bent into a continuously deforming concave shape. To approximate such an arm with a polygonal mesh for collision detection is expensive not only because a fine mesh is required to approximate concavity but also because each time the manipulator deforms, a new mesh has to be built for the new configuration. However, most generic collision detection algorithms apply to only polygonal meshes or objects of convex primitives. In this paper, we propose an efficient algorithm for Collision Detection between an Exact Continuum Manipulator (CD-ECoM) and its environments, which is applicable to any continuum manipulator featuring multiple constant-curvature sections. Our test results show that using this algorithm is both accurate and more efficient in both time and space to detect collisions than approximating the continuum manipulator as polygonal meshes and applying an existing generic collision detection algorithm. Our CD-ECoM algorithm is essential for path/trajectory planning of continuum manipulators.