A method is presented in which the axial viscoelastic response of a multiple filament strand, constrained by a no-end rotation boundary condition, may be predicted. This method is an initial attempt to describe the time-dependent response of the multilayer strand by incorporating the stress relaxation data for a linearly viscoelastic construction material. Specifically, a strand consisting of a core filament, six filaments in the second layer, and twelve filaments in the outer layer is analyzed. This analysis could, however, include any number of layers of filaments where each layer has a concentric helix radius. The particular material used in this paper is polymethyl methacrylate (PMMA). The stress relaxation for PMMA is modeled analytically using the Schapery collocation method which determines the constant coefficient values for the elements of a Wiechert response model. Since this is a first approximation model, the approach is limited to linear viscoelasticity. The geometric effects of the strand are then combined with the Wiechert response model to develop a system of convolution integrals which satisfy the equilibrium and imposed boundary conditions for the multiple filament strand construction. The solutions for these integrals are approximated numerically using a modified Newton’s iterative method combined with a numerical technique which takes into account the material’s stress-strain history.