Scanning tunneling microscopy is used to study beta-SiC (001) and (111) surfaces. The (001) surfaces of beta-SiC were grown on Si(001) substrates while the (111) surfaces were grown on alpha-SiC{0001} substrates, both by chemical vapor deposition. The surface morphology for the beta-SiC(001) surface grown on Si(001), the beta-SiC(111) surface grown on Si-terminated alpha-SiC(0001), and the beta-SiC(111) surface grown on C-terminated alpha-SiC(0001BAR) are compared. Atomically resolved images of the c(2 X 2) and (3 X 2) reconstructions of the beta-SiC(001) surface and the honeycomblike reconstruction on the beta-SiC(111) surface are presented.