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This work presents impedance functions for inclined pile groups embedded in different half spaces whose stiffness continuously increases with depth. The results are obtained through a three-dimensional harmonic model where the soil response is modelled through the reciprocity theorem in elastodynamics and the use of Green’s functions for the layered half space, while the piles are represented by finite elements as Timoshenko’s beams. Linear behaviour of soil and piles is assumed. The use of several normalization schemes for the representation of the impedance functions is discussed, highlighting the benefits and drawbacks of each choice and their effects on the interpretation of the obtained results. As a result, expressions for the dimensionless impedance functions and frequency are proposed in order to synthesize the results of the different soil profiles into the same curves. The final objective of the proposed normalization is to transform the well-known impedance functions for the homogeneous halfspace into the corresponding curves for a specific non-homogeneous profile that can be used, e.g., in a substructuring methodology. Despite the fact that the presence of soil non-homogeneity increases the dependence of the impedance functions on the frequency, good agreements between the homogeneous and non-homogeneous profiles can be achieved for a range of frequency of interest. [ABSTRACT FROM AUTHOR]