The finite-element (FE) method is used for modeling geotechnical and pavement structures exhibiting significant non-homogeneity. Property gradients generated due to non-homogeneous distributions of moisture is one such example for geotechnical materials. Aging and temperature-induced property gradients are common sources of non-homogeneity for asphalt pavements. Investigation of time-dependent behavior combined with functionally graded property gradation can be accomplished by means of the non-homogeneous viscoelastic analysis procedure. This paper describes the development of a generalized isoparametric FE formulation to capture property gradients within elements, and a recursive formulation for solution of hereditary integral equations. The formulation is verified by comparison with analytical and numerical solutions. Two application examples are presented: the first describes stationary crack-tip fields for viscoelastic functionally graded materials, and the second example demonstrates the application of the proposed procedures for efficient and accurate simulations of interfaces between layers of flexible pavement. Copyright (c) 2011 John Wiley & Sons, Ltd.