Abstract: The paper proposes a scheme by combining the Runge–Kutta discontinuous Galerkin method with a $\delta$-mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes. This hybrid scheme is particularly applied to nonlinear elasticity in heterogeneous media and multi-class traffic flow with inhomogeneous road conditions. Numerical examples indicate the scheme's efficiency in resolving complex waves of the two systems. Moreover, the discussion implies that the so-called $\delta$-mapping algorithm can also be combined with any other classical methods for solving similar problems in general.