Pyrolysis of waste plastics is one method currently being investigated as an alternative to landfill disposal of this increasingly large waste stream. Although the pyrolysis process produces significant quantities of Light naphtha range liquids, there is also a residual fraction that may be considered as a potential feedstock for upgrading. The objective of our research was to investigate the upgrading potential of the gas oil fraction of a typical plastics pyrolysis Liquid using catalytic hydrocracking, in this study, the residual fraction of a liquid produced by the pyrolysis of plastics, containing about 70%, +205 degrees C gas oil, was subjected to batch hydrocracking reactions. The reactions used a commercial NiMo supported on zeolite-alumina catalyst and gave good conversion to naphtha. A simplified three-lump sequential reaction pathway (gas oil --> naphtha --> gas) was applied to simulate the upgrading of the gas oil fraction to naphtha and gases. The kinetic model considered the variation in Ha partial pressure in the hydrocracking rate expression and thereby was able to account for conversion and yield differences between large and small batch reactors. The model simulated the experimental data well including experimentally observed trends such as the maximum in naphtha yield at lower temperatures.