Various theoretical techniques have been devised to determine distribution functions of particles accelerated by the first-order Fermi mechanism at collisionless astrophysical shocks. The most stringent test of these models as descriptors of the phenomenon of diffusive acceleration is a comparison of the theoretical predictions with observational data on particle populations. Such comparisons have yielded good agreement between observations at the quasi-parallel portion of the Earth's bow shock and three theoretical approaches, namely, Monte Carlo kinetic simulations, hybrid plasma simulations, and numerical solution of the diffusion-convection equation. Testing of the Monte Carlo method is extended in this paper to the realm of oblique interplanetary shocks: here observations of proton and He2+ distributions made by the SWICS ion mass spectrometer on Ulysses at nearby interplanetary shocks (less than about 3 AU distant from the Sun) are compared with test-particle Monte Carlo simulation predictions of accelerated populations. The plasma parameters used in the simulation are obtained from measurements of solar wind particles and the magnetic field upstream of individual shocks; pickup ions are omitted from the simulations, since they appear, for the most part, at greater heliospheric distances. Good agreement between downstream spectral measurements and the simulation predictions are obtained for two shocks by allowing the parameter lambda /rg, the ratio of the mean-free scattering length to the ionic gyroradius, to vary in an optimization of the fit to the data; generally lambda /rg <~ 5, corresponding to the case of strong scattering. Simultaneous H+ and He2+ data, presented only for the 1991 April 7 shock event, indicate that the acceleration process is roughly independent of the mass or charge of the species. This naturally arises if all particles interact elastically with a massive background, as occurs in collisionless "scattering" off a background magnetic field, and is a patent property of the Monte Carlo technique, since it assumes elastic and quasi-isotropic scattering of particles in the local plasma frame.