A two-dimensional solar prominence model is extended to three-dimensional variations and curved current sheets. The model treats prominences as infinitely thin electric current sheets forming vertical planes supported by a magnetic potential. Equilibrium states are derived by solving Ampere's equation for a discrete current density of a surface where the Lorentz force is everywhere upward. The mass distribution is calculated to balance the Lorentz force. Linear superpositions of potential fields are employed to define three-dimensional models for periodic prominences in a given direction and for a prominence mass sheet with a finite length. 22 references.