Results of two-dimensional electrostatic modeling of organic field-effect transistors, focusing on the formation of the conductive channel, are reported. The effect on channel formation of the choice of the source and drain contact metal is investigated for both top- and bottom-contact device structures. High-work-function metal (e.g., gold) source and drain contacts produce a conducting p-type region near these contacts. In contrast, low-work-function metal source and drain contacts (e.g., magnesium) lead to depleted regions. In the center of the device, between the source and drain contacts, the channel carrier density at a fixed gate bias is determined by the work function of the gate contact material, and is essentially independent of the metal used to form the source and drain contacts. The principal difference between top- and bottom-contact structures is the spatial variation of the charge density in the vicinity of the source and drain contacts. The channel carrier density for a fixed gate bias (and gate contact material) between the source and drain electrodes is essentially the same for the two structures. Finally, the dependence of the transistor threshold voltage on the gate contact metal work function and the device implications of the spatial variation of the induced charge density are discussed.