The evaluation of the source rock is based on the source rock richness, maturation and thermal burial history. The present study aims to construct a two-dimensional model of burial history and thermal evolution for the Miocene and pre-Miocene rocks, penetrated by eight wells in Shoab Ali Oil Field, to illustrate the effect of time and temperature on the oil generation and maturation level of organic matter. Our reconstructions of the thermal history took into account processes such as: a) variable rates of sedimentation and consolidation of the porous rocks, b) erosion and interruption of sedimentation, c) change of thermophysical characteristics with lithology, depth and temperature of rocks and, d) dependence of water, matrix and mantle heat conductivity on temperature. The evaluation of the hydrocarbon-generation potential in the study area is achieved by using the wireline log analysis as a semi-quantitative method for determination of the organic matter concentration (by volume %). Moreover, a number of iso-parametric maps are drawn to show the horizontal distribution of the geothermal gradient and the total organic carbon content (TOC) of the investigated area. The results of this evaluation study show that the Miocene shale and argillaceous limestone are a variably poor to good source rock, while the Pre-Miocene rocks (Thebes, Esna, Sudr, and Matulla Formations) are good to very good source rocks.