  We have developed a Monte Carlo technique for self-consistently calculating
the hydrodynamic structure of oblique, steady-state shocks, together with the
first-order Fermi acceleration process and associated non-thermal particle
distributions. This is the first internally consistent treatment of modified
shocks that includes cross-field diffusion of particles. Our method overcomes
the injection problem faced by analytic descriptions of shock acceleration, and
the lack of adequate dynamic range and artificial suppression of cross-field
diffusion faced by plasma simulations; it currently provides the most broad and
versatile description of collisionless shocks undergoing efficient particle
acceleration. We present solutions for plasma quantities and particle
distributions upstream and downstream of shocks, illustrating the strong
differences observed between non-linear and test-particle cases. It is found
that there are only marginal differences in the injection efficiency and
resultant spectra for two extreme scattering modes, namely large-angle
scattering and pitch-angle diffusion, for a wide range of shock parameters,
i.e., for subluminal shocks with field obliquities less than or equal to 75
degrees and de Hoffmann-Teller frame speeds much less than the speed of light.
