A method for numerical solution of the continuous spectrum linear biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. The method is based on an alternate formulation of the continuous spectrum stress-strain law that is implemented using Gaussian quadrature integration combined with quadratic interpolation of the strain history. For N time steps, the cost of the method is O(N). The method is applied to a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. For a range of relaxation times that are representative of articular cartilage, accuracy of the method is demonstrated by direct comparison to a theoretical Laplace transform solution.