A flexible composite tube for medical applications is described. The tube has the ability to transmit a torque and to resist compression, tension, and kinking. The tube is also very flexible in bending, and has a small wall thickness. Different layers are used to obtain the desired properties. Torsional stiffness is obtained by embedding a braid in an elastomeric material. Resistance to kinks and to compression and tension is obtained by placing coils radially inward or outward of the braid. Smooth plastic layers are used to seal the assembly, and facilitate sliding in a body cavity.