We introduce a modified particle method for semi-linear hyperbolic systems with
highly oscillatory solutions. The main feature of this modified particle method is that we do not
require different families of characteristics to meet at one point. In the modified particle method,
we update the ith component of the solution along its own characteristics, and interpolate the other
components of the solution from their own characteristic points to the ith characteristic point. We
prove the convergence of the modified particle method essentially independent of the small scale for
the variable coefficient Carleman model. The same result also applies to the non-resonant Broadwell
model. Numerical evidence suggests that the modified particle method also converges essentially
independent of the small scale for the original Broadwell model if a cubic spline interpolation is used.