We use semianalytic methods to model a periodic structure of plate-array cylinders (metacylinders), and derive several of the medium's effective material properties in the quasistatic limit. Subject to 𝑠-polarized [transverse-electric (TE)] light, the anisotropic dispersion of the crystal manifests as a Maxwell Garnett equation for the effective permittivity at leading order. This is performed both for the case of no material contrast between interior and exterior regions, and a nonunity normalized refractive index. In each case, the leading order effective permittivity is a function of the difference between Bloch wave and plate-array angles. As such, we envisage the metamaterial as being mechanically tunable through uniform mechanical rotation of the constituent metacylinders.