Recent observations of Martin, Bilimoria, and Tracadas (1995) have revealed two new magnetic and structural classes for solar filaments and filament channels. The magnetic classes are called sinistral and dextral, while the structural classes are left-bearing and right-bearing. Dextral filaments dominate in the northern hemisphere and sinistral in the southern. A model consistent with the observations is developed with magnetic sources that represent the network flux on both sides of the channel and extra concentrations of flux that produce the strong field component along the channel. We suggest that it is the imbalance of flux locations along the channel that creates the field of a filament channel. The resulting separatrix surfaces have distinct upper and lower boundaries that may produce the upper boundary of the filament cavity or filament and the lower boundary of the filament. The model is applied to a specific filament channel, with discrete sources and sinks that represent the flux observed in a photospheric magnetogram. The resulting three-dimensional field lines near the filament location are low-lying and possess dips.