The Intermittent Gas Lift (IGL) is an artificial lift method for petroleum production suitable for producing wells from depleted or low productivity reservoirs. In order to enhance the well production, many variants of the conventional IGL have been developed and used worldwide. One of these variants, the Inverted IGL (IGL-I), consists of removing the gas lift valve and reversing the flow paths inside the well: gas is injected through the tubing whereas liquid is lifted through the casing annulus. The oil production is believed to increase with the IGL-I due to the larger annulus storage capacity, at the expense of higher injected gas volumes. Despite of its potential for practical applications, the IGL-I has not been covered by the literature. Aiming to surmount such gap in the literature, this paper presents a model for the dynamical behavior of the IGL-I wells. The complexity emerged from the IGL-I cyclic operation is assessed through a simultaneous and coupled simulation scheme, comprising a variable set of non-linear algebraic equations and non-linear time-differential equations for the flow of oil and gas throughout the injection, transfer, elevation, production, decompression and loading stages of each cycle. The simulator provides the engineer with a valuable tool to investigate the well behavior of several IGL cycles. Based on the observed results, the designer may propose practical recommendations regarding the IGL-I design and operation.