Numerical simulations of organic field-effect transistors (OFET) of bottom and top contact (BOC, TOC) design with different source/drain contacts were carried out considering an exponential distribution of trap states in the gap of the active layer (a-Si model). For ohmic contacts, the current-voltage characteristics are similar to the trap-free case and there is not much difference between the two designs. However, the currents are lower due to immobile trapped charges, the threshold voltage is shifted, and the inverse subthreshold slope increases due to trap recharging. An analytical approximation for the effective mobility deviates from the simulation up to 20%. For low source/drain work function, there occur particular dependencies of the current on the gate voltage for the two designs, which are explained with the internal concentration and field profiles. A series resistance between source and channel causes in the TOC structure an abrupt transition from the gate voltage independent active region into saturation. In the BOC case, the reverse-biased Schottky-type source contact dominates the current. Through simulation of measured characteristics of prepared OFETs based on a modified poly-(phenylene-vinylene), the observed hysteresis is analyzed.