For both even and odd-numbered solar cycles, right-hand heliform filaments predominate at middle and high latitudes in the northern hemisphere while left-handed ones predominate in the south. This recent discovery has prompted a re-examination of past measurements of magnetic fields in prominences. This re-examination indicates that Rust (1967), in his interpretation of solar cycle 20 measurements in terms of the Kippenhahn-Schlüter model, and Leroy, Bommier, and Sahal-Bréchot (1984), in their interpretation of solar cycle 21 measurements in terms of the Kuperus-Raadu model were both misled by the global pattern of helicity. While the original magnetic field measurements are consistent with the new results about heliform magnetic fields in filaments, neither of the well-known classes of two-dimensional models can produce both the proper axial field direction and the observed pattern of helicity. A global, subsurface velocity pattern that would twist the fields before emergence as filaments seems to be required. In this paper a twisted-flux-rope model consistent with the new understanding of filament fields is presented. The model is based on a constant-α solution of the magnetostatic equations, where electric current densityj(r) =α B(r). The model filament has dimensions in general agreement with observations. It is shown to be stable if the length is less than 140 000 km to 1,400 000 km, depending on the value ofα. The model also provides a new explanation of eruptive prominences and for the origin of the entrained material.