The evolution of pore pressure including overpressure during sedimentation is an important process to consider when analyzing whether high pore pressure causes rock failure. High pore pressure is caused by under-compaction due to the rapid burial of low-permeability sediments, and as a result, porosity decreases less rapidly with depth than in normally compacted sediments where porosity decreases exponentially with depth. While under-compaction related pore pressure magnitudes have been determined empirically, in most numerical modeling approaches, the pore pressure is either applied as a static magnitude or coupled to a fluid flow simulator. This study simulates the pore pressure evolution during sediment loading and compaction using 3D porous-elastic-plastic finite element analysis. Continuous sedimentary loading is applied, and the resulting compaction process is coupled to the evolution of Poisson ratio and bulk modulus. The models test compacted sandstone and shale beds with varying ranges of physical properties including porosity, permeability, and elasticity for various sedimentation rates and initial physical properties distributions. Initial results show that overpressure occurs in rock layers with a permeability lower than 10-12 m2 when the sedimentation rate is equal to or exceeds 10 mm/year. It also shows that porosity tends to either decrease much slower or temporarily stops decreasing with the development of overpressure. Porous space is easier to be compacted in rocks featuring a lower bulk modulus under the same effective stress. The presented procedure enables to couple the simulation of the effective state of stress both due to the initial burial history of a sedimentary basin therefore provides a better assessment for rock failure analysis --Abstract, page iii