The constitutive dielectric parameters for uniform space arrays of generalized structural geometry composed of similarly oriented elements of completely generalized material and shape are derived. The theoretical procedure employed in evaluating these parameters is analogous to the classical method applied to the study of the dielectric properties of nonpolar media and assumes that the disturbing action of each particle on a uniform static field can be allowed for, if each particle is replaced by a set of dipoles. Consequently, the results are applicable to microwave frequencies only if the cross‐sectional dimensions and interelemental spacings remain small compared to the wavelength. The general result is particularized for the case in which the elements are spherical objects with a tensor permeability and scalar dielectric constant. The results have several applications to the design of artificial dielectrics and some of these are given.