Solid modeling underlies many technologies that are key to modern manufacturing. These range from com puter-aided design systems to robot simulators, from finite element analysis to integrated circuit process modeling. The accuracy, and hence the utility, of these models is often constrained by the amount of com puter time required to perform the desired operations. We present a family of algorithms for solid modeling operations using the Connection Machine, a massively parallel SIMD processor. We describe a data structure for representing solid models and algorithms that use the representation to implement efficiently a variety of solid modeling operations. We give a sketch of the al gorithm for intersecting solids and present computa tional experience using these algorithms. The data structure and algorithms are contrasted with those of serial architectures, and execution times are compared. © 1992, Sage Publications. All rights reserved.