Equations are derived for the electric potential and field intensity due to a distribution of space charge in a slab of dielectric between two infinite parallel conducting plates. The charge density may be any integrable function of the coordinate perpendicular to the plates. The corresponding solution for concentric cylinders is also given. A number of special cases are discussed, including that of a uniformly distributed charge, and one of sinusoidal distribution. The latter has an application in the theory of the piezoelectric resonator.