Abstract: Yielding behaviors of waxy crude oil is one of the key issues of flow assurance challenges. The yielding of waxy crude under constant stress is actually a creep process of strain accumulation to structural failure, to describe the process completely and accurately is the basis of numerical simulation of restart process of the pipeline. The creep and yield behaviors of two gelled waxy crudes were investigated experimentally under different constant applied stresses. The results clearly show that the creep process of waxy crude is related to the applied stress and time. The greater the applied stress, and the longer the loaded time, the more obvious the nonlinear features. Based on the fractional calculus theory, a fractional viscous element was developed to describe the decelerated and steady creep process of gelled waxy crude. On the basis of the damage theory, an elastic damage element was proposed to describe the accelerated creep after the yielding. According to the idea of mechanical analogy, a nonlinear creep model was established by a fractional viscous element, an elastic damaged element, and an elastic element in series, which can accurately describe the whole creep and yielding process of gelled waxy crude.