In this work, we present the development of a mathematical approach for the solution of linear, non-ageing viscoelastic materials undergoing mechanical deformation. We use an integral approach based on a discrete spectrum representation for the creep tensor in order to derive the incremental viscoelastic formulation. Integral operators are discretized using finite difference techniques. The incremental viscoelastic consti-tutive model contains an internal state variable which represents the influence of the whole past history of stress and strain, thus the difficulty of retaining the stress-strain history in numerical solutions is avoided. A complete general formulation of linear viscoelastic stress-strain analysis is developed in terms of increments of stresses and strains. Numerical simulations are included in order to validate the incremental constitutive equations.