We present an analysis of artificial dielectric layers (ADLs), when a lateral shift between layers is present. The alternate lateral displacement of the layers is an important parameter to engineer the desired effective electromagnetic properties of the ADL material. More specifically, much higher equivalent dielectric constants can be realized by alternatively shifting the layers, compared to the aligned case. Closed-form expressions are given for the equivalent layer reactance that include the higher-order interaction between shifted layers. These analytical formulas can be used to design artificial dielectric slabs, as they provide the scattering parameters for generic plane-wave incidence.