We present a model for the quantitative assessment of the influence of crystal defects on the piezoresistive properties of n-type cubic silicon carbide. In an extended carrier trapping model, the strain dependent transport at potential barriers formed by electrons in defect states at internal boundaries is calculated. Based on experimental results of electronic and structural characterization, the piezoresistive properties of nanocrystalline silicon carbide are derived. The magnitude of the piezoresistive gauge factor as well as its dependence on temperature, carrier density, and crystal orientation shows excellent agreement with the experimental findings. Taking the depth profile of the defect density into account, the same model is used to explain the depth dependence of the piezoresistive gauge factors in single crystalline cubic silicon carbide layers.