Coefficients of characteristic polynomials for stable parametrically uncertain systems are allowed to perturb to some extent for stability. Stability radius is a useful tool to assess the allowance of the stability for the systems. To enhance its usefulness, we modify stability radius so that it takes into account of given restricted perturbations, which we call directional stability radius. For an application, we show shifted-Hurwitz stability conditions and a stability analysis method for interval polynomial systems using the directional stability radii.