The cubic silicon carbide (3C-SiC) has broad application prospects in many fields due to its excellent material properties. The modeling of damage in 3C-SiC due to contact loads is important yet challenging. In this paper, simulations based on ordinary state-based peridynamics (PD) theory are proposed to model the damage of 3C-SiC in indentation and scratching. The constitutive parameters of 3C-SiC for PD simulation are obtained by performing MD simulations of nanoindentation. It is found that in the indentation simulations the initiation and propagation of cracks are observed, which shows that the PD can model the crack formation and propagation in the indentation process of brittle solid materials. During the scratching process, the variation of friction force is consistent with that of material wear. It is also found that the specific cutting energy increases nonlinearly with the decrease of scratching depth due to size effect. In addition, for the scratching with double indenters, the volume of material removal is more than twice that of scratching with an indenter due to the coupling effect of the two indenters under certain conditions. This paper demonstrates that PD is a powerful tool to investigate the indentation and scratching process of brittle solid materials.