An analytical model incorporating the density of trap states for a bendable organic field effect transistor (OFET) is presented in this paper. The aim of this work is to propose a novel modeling framework to quantitatively characterize the bending effects on the electrical properties of an OFET in the linear and saturation regimes. In this model, the exponentially distributed shallow trap states are introduced into the Poisson equation to describe the carrier transports in the channel. The carrier mobility takes into account the low field mobility enhancement under gradual channel approximation and high field degradation. As a result, the generalized current-voltage transistor equations are derived for the first time to reflect the transconductance relationships of the OFET with trap states. In addition, an electro-mechanical coupling relationship is established per the metaphorical analogy between inorganic and organic semiconductor energy band models to quantify the stress-induced variations of the carrier mobility, and the threshold voltage. It is revealed that the before- and after-bending transconductances, predicted from the derived analytical model, are in good agreement with the experimental data measured from DNTT-based OFET bending tests.