Petrographic characteristics (textural properties and modal compositions) have an intrinsic influence on the physical and mechanical (PM) properties of weakly cemented sandstones. Sixteen sandstone samples were tested to determine the PM parameters and then thin sections from those samples were used to measure the petrographic parameters. Petrographic parameters were analysed statistically to establish quantitative relationships between the petrographic characteristics and PM properties. Based on multiple linear regression (MLRA) and stepwise multiple regression analyses (SMRA), several multiple regression equations with significant petrographic variables were established for estimating the PM parameters of the sandstone. Results indicated that uniaxial compressive strength (UCS) and Young's modulus (E) were closely related to mean grain size (Mz) (φ-value), non-uniform coefficient (Cu), fractal dimension (Fd), Riley sphericity (Ψp), packing proximity (Pp), floating contacts (Fl), grain-to-grain contacts (G-G), feldspar content and organic matter content. An increased percentage of grain-to-cement contacts (G-C) and reduced percentages of grain-to-matrix contacts (G-M) and organic matter content indicated a high value of Poisson's ratio (POISS). In addition, Mz, Cu, Fd, Ψp, quartz, feldspar, and organic matter contents were found to be significant parameters for density and P-wave velocity (Vp). Furthermore, density and POISS could be predicted using the results from the MLRA and Fd was a good predictor for density, Vp and UCS using the results from the SMRA. Additionally, it was noted that the petrographic characteristics of roof sandstones had significant influence on the overburden pressure characteristics within the coal faces in the Shendong mining area.