Abstract One of the most successful long-stroke pumping units available today is the Rotaflex, a completely mechanical device. Its construction is entirely different from the traditional beam pump mechanisms and has polished rod stroke lengths up to 366 in. Due to the low pumping speeds required and the special geometrical arrangement Rotaflex units require significantly less torque than beam pumping units and provide several other advantages over those. The unit's most important component is a uni-directionally rotating roller chain connected to the polished rod through an elastic load belt. The kinematic behavior of the chain, running on two sprockets is relatively simple to describe; the paper presents exact formulae for the calculation of polished rod position, velocity, acceleration, and torque factor functions. The recommended formulae provide a theoretically sound description of the unit's kinematic behavior and can serve a sound basis for the calculation of gearbox torques for cases when load belt stretch is neglected. Prior publications on Rotaflex operations relied on the assumption of a rigid load belt and determined the loading of the gearbox accordingly; field practice, however, indicates considerable stretch in the elastic belt. The paper, for the first time, presents a thorough investigation of the kinematic performance of Rotaflex pumping units with due consideration of belt stretch. The effect of operational stretch due to polished rod load on gearbox torques and the energy conditions of Rotaflex units is investigated through several example problems.