This paper investigates the differential stability of parametric bang–bang control problems governed by semilinear elliptic partial differential equations. Under some standard assumptions in optimal control theory, we establish exact formulas for computing the regular subdifferential, the Mordukhovich subdifferential, and the singular subdifferential of the marginal function of the parametric bang–bang control problems. The obtained results of subdifferential calculations deduce the local Lipschitzian property of the marginal function.