A tight-binding model Hamiltonian is newly parametrized for silicon carbide based on fits to a database of energy points calculated within the density functional theory approach of the electronic energy surfaces of nanoclusters and the total energy of bulk 3C and 2H polytypes at different densities. This TB model includes s and p angular momentum symmetries with nonorthogonal atomic basis functions. With the aid of the new TB model, minima of silicon carbide cagelike clusters, nanotubes, ring-shaped ribbons, and nanowires are predicted. Energetics, structure, growth sequences, and stability patterns are reported for the nanoclusters and nanotubes. The band structure of SiC nanotubes and nanowires indicates that the band gap of the nanotubes ranges from 0.57 to 2.38 eV depending on the chirality, demonstrating that these nanotubes are semiconductors or insulators. One type of nanowire is metallic, another type is semiconductor, and the rest are insulators.