Gas cyclic pressure pulsing is an effective EOR method in naturally fractured reservoirs. A limited number of studies concerning this method in the literature focuses on specific reservoirs and the optimum operating conditions have not been broadly investigated. In this study, we present a detailed parametric study of the process from both operational and reservoir perspectives. Incremental oil production, peak oil rate and net present value (NPV) are considered as the important markers for the performance criteria. The necessary analyses are performed for a single-well, dual-porosity, compositional reservoir model. In the first part of the study, parametric studies are conducted to develop a better understanding of the operational parameters affecting the process performance, in the shallow, naturally fractured, and depleted reservoirs of Big Andy Field in Eastern Kentucky. These include analyses of various design parameters such as soaking period, cycle rate limit, number of cycles, cycle and cumulative injected gas volumes. In the second part of the study, reservoir characteristics are investigated. Comparative discussions are presented between cases with CO2 and N2 as the injected gas on reservoir fluids of different compositions (heavy, black and volatile oils). Influences of area, thickness, fracture/matrix permeabilities, initial reservoir pressure and temperature on the process are studied. It is observed that N2, as a lower-cost gas, would be a better choice than CO2 in the Big Andy Field. With the oil price used in this study, the cost of injected gas becomes relatively insignificant in economic considerations. Increased income due to increased oil production overcomes the increased costs with higher volumes of gas. The way reservoir characteristics affect the process performance is very similar in cases with CO2 and N2, but differs significantly in different reservoir fluids. Thicknesses ranging between 20 and 50 ft produced more favorable results. A higher efficiency was observed with smaller drainage areas (5-8 acres) in the presence of heavy oil. For the cases with volatile and black oil, it is seen that the process efficiency is not significantly altered by the area. The phase behavior of the reservoir fluid is very important for the performance of the process. Initial pressure/temperature of the reservoir, and therefore, the initial fractions of gas/liquid phases affect the process efficiency in a more pronounced manner.