Conventional composite materials have high stiffness-to-weight ratios but exhibit little damping; many viscoelastic materials provide high levels of energy dissipation with minimal structural stiffness. The objective of this work was to combine these two material types to produce highly damped structural elements with favorable stiffness and weight characteristics. Cocuring refers to the inclusion of one or more layers of viscoelastic damping material sandwiched between composite plies prior to curing of the composite. Cocured viscoelastic/composite layups were studied experimentally at the material level, modeled analytically, and used to build optimized damped structural components. Measured cocured material properties were used in finite element models to design damped components which were built and tested individually and as part of a truss test structure. Load-carrying and highly damped struts and panels were fabricated. The curing process modified the viscoelastic behavior to some degree, but the materials retained significant, and predictable, damping capability.