The flow of suspensions flocculated by reversible bridging of polymer with weak affinity for the particle surface is Newtonian in the limit, of zero shear rate, shear-thickening at moderate shear rates, and plastic implies the polymer bridges are constantly forming and breaking in a quiescent state. The stress after cessation of steady shear exponentially relaxes at long times. The relaxation time is not affected, by the sheer rate. The strain-dependent curve of storage modulus at a constant frequency shows a rapid increase when the strain is increased above a critical level. The critical strain is independent of frequency. Therefore, the shear thickening may be primarily attributed to the elastic effect of extended bridges. Since the polymer coils are forced to desorb at some degree of extension, the suspensions become nearly plastic at high shear rates. The intrinsic mechanism of sheer-thickening flow far suspensions flocculated by reversible polymer bridging is the nonlinear elasticity due to entropy effect of extended bridges and forced desorption due to hydrodynamic effect. By combination of the nonlinear elasticity and single relaxation time, a rheological model is derived to quantitatively express the shear-thickening flow. The model prediction and experimental results are in good agreement.