Monte Carlo particle transport is an inherently parallel computational method that has been successfully implemented on diverse computational platforms such as vector processors, shared memory and distributed memory Multiple Instruction, Multiple Data (MIMD) parallel processors, multiple vector processors, and Single Instruction, Multiple Data (SIMD) parallel processors. Vectorizing a Monte Carlo algorithm requires a major change in the algorithm and coding; but the performance gain due to vectorization can be significant and once vectorized it is relatively easy to parallelize across multiple vector processors. Parallelizing a Monte Carlo code is relatively easy, and the continuing decrease in the costs of massively parallel processors (MPPs) makes it attractive to adapt to a MPP. In this chapter we describe the effort to adapt two classes of Monte Carlo particle transport algorithms on different parallel machines. We provide details of the two parallel algorithms, including modifications to the random number generator, and will present wall clock timing results on different parallel architectures. The first algorithm is intended for a fixed source application and simulates photon transport in a high temperature plasma. The second algorithm is intended for the calculation of eigenvalues and perturbations in eigenvalues for neutron transport problems. The following constraint has been imposed on both parallel algorithms - the Monte Carlo simulation should yield identical results for runs with the same number of tasks, independent of the number of CPUs which are actually executing these tasks. This is a generalization of the principle of reproducibility, an essential characteristic of particle transport Monte Carlo codes.