Summary: A data parallel implementation of the finite element method on the Connection machine system CM-2 is presented. This implementation assumes that the elementary unit of data is an unassembled nodal point. In the context of the CM-2, each virtual processor repesents an unassembled nodal point and nodal points shared between elements are replicated on different virtual processors. An algorithm for computing each elemental stiffness matrix concurrently, as well as different elemental stiffness matrices concurrently, without inter-processor communication is presented. The performance of the elemental stiffness matrix computation is in the range 1.6-1.9 GFlops \(s^{-1}\). The sparse system of linear equations that results from the finite element discretization has been solved by a conjugate gradient method with a diagonal preconditioner. The rate of convergence of the conjugate gradient iterations for boundary conditions which correspond to uniaxial deformations depends nonlinearly on the order of interpolation of the elements and linearly on the mesh discretization. Sample code segments are provided to illustrate the programming environment on a data parallel architecture.