In this paper, mechanical properties and buckling behavior of single-walled silicon carbide nanocones (SWSiCNCs) are studied using a finite element method. The elastic moduli of SWSiCNCs with different dimensions including different apex angles and lengths are presented. For large apex angles, it is shown that the effect of nanocone length on the elastic modulus can be neglected. Besides, the critical compressive forces of SWSiCNCs are computed. The influences of dimensions and boundary conditions on the buckling behavior of SWSiCNs are studied in detail. The results show that increasing the nanocone apex angle leads to decreasing the critical compressive force.