Molecular dynamics simulations with the Tersoff potential were used to study the response of twinned SiC nanowires under tensile and compressive strain. The critical strain of the twinned nanowires can be enhanced by twin stacking faults, and their critical strains are larger than those of perfect nanowires with the same diameters. Under axial tensile strain, the bonds of the nanowires are stretched just before failure. The failure behavior is found to depend on the twin segment thickness and the diameter of the nanowires. An atomic chain is observed for thin nanowires with small twin segment thickness under tension strain. Under axial compressive strain, the collapse of twinned SiC nanowires exhibits two different failure modes, depending on the length and diameter of the nanowires, i.e., shell buckling for short nanowires and columnar buckling for longer nanowires.