The atomic-level description of a complex heavy hydrocarbon feedstock and its complete temporal product behavior is a challenging and computationally intensive problem which requires robust reaction simulations to accurately account for kinetic interactions and efficient utilization of available computer hardware for solution. Herein we discuss the parallel implementation of different Monte Carlo reaction algorithms for two prototype kinetic problems and examine their efficiency on MIMD and SIMD parallel architectures. The concepts developed are subsequently applied to a complex resid pyrolysis model. Both fixed- and variable-time step Monte Carlo approaches to the stochastic simulation algorithm were investigated. The prototype kinetic problems consisted of Ai⇌Bi with Ldngmuir-Hinshelwood-Hougen-Watson kinetics for i = 1-3 and a hypothetical 1-5 ring aro matic hydrogenation simulation. The two parallel architectures utilized were BBN's TC2000 (MIMD) and Thinking Machines CM-2 (SIMD). A new modelling approach that stochastically samples the reaction environment to provide an estimate of species' interactions is introduced. This "partial system" approach exhibited excellent parallel efficiency ( > 90%) on the TC2000. The simple prototype Ai⇌Bi kinetic problem was also successfully implemented on the SIMD CM-2. While the 1-5 ring hydrogenation problem efficiently took advantage of the MIMD architecture, its performance on the CM-2 was quite poor due to the the lack of a match between the data focus of complex model simulations and the CM-2 data parallel paradigm. The resid pyrolysis model performed extremely well on the MIMD machine.