Shape memory materials (SMM) are formed as coil-shaped vascular occlusion devices upon deployment. Shape memory polymer (SMP) materials are tailored through formulation for specific mechanical behavior of the coils. Concurrent coil diameter changes enhance the relative change in stiffness along the length of the coil. Interconnecting structures (104a/b) are formed on ends of elongated members (102a) in the pre-deployment shape for multiple coil insertion capability within an introducer. Channels (206) are formed in pre-deployment shape, elongate members (202) that allow access for injection of imaging contrast agent or concurrent placement of instruments. A single SMM occlusive device (300) transforms into multiple, smaller diameter coils (302b) in the deployed state to generate a complex occlusive structure. A SMM occlusive device (400) has a collapsed fabric (404) component attached to and extending along a sidewall during storage and insertion, and then deploys as a coil (402b) to form a single- or multiple-layer occlusive fabric surface within a center of the coil (402b).