The Langlands-Rapoport conjecture gives a description of the mod $p$ points of suitable integral models of Shimura varieties. Such results are of use, for example, in computing the local factor of the (semi-simple) Hasse-Weil zeta function of the Shimura variety. In this talk, we show that the points in each of the isogeny classes on the special fiber of the integral models of Shimura varieties with parahoric level constructed by Kisin and Pappas have the form predicted by the above conjecture, when the group is residually split at p. Along the way, we verify some of the He-Rapoport axioms which allow us to deduce the non-emptiness of Newton strata for these models.