Theis paper deocument the use of a massively parallel computer, specifically the connection machine CM-5 , to solve the boltzmann equation to model one-dimensional shcok wave strcture, a boudnary laryer, and general 3D flow fields. The Bhatnagar-Gross-Krook (BGK) model for the collision term combined with a finite differnce scheme was used to model flow. Thies collision rerm requires accurate knowledge of the density, temperatur, and mean volecity. Great care must be taken in their calculatin to insure conservation, which proved to be the most difficult part. The algorithm, however, is well suited to the conncetion machine, and accurate results were obtained with great efficiency. THe I-D version of the code ( witch actually models a 5-D problem in phase space) was optimized for the CM-5 and sustained 61 gigaflops on a 1024-node CM-5