Time-dependent wellbore (in)stability during oil and gas drilling account for a significant amount of lost rig time and substantially increased drilling costs ($700 million annually according to conservative estimates). Coupled time-dependent processes have been previously described in the realm of the poroelasticity theory. This wellbore (in)stability modeling approach allows the drilling engineer to systematically include the stress variation around the wellbore and the associated rock deformation and pore pressure changes. In this paper, in addition to the analyses conducted on the previously derived solutions for thermal and pore fluid diffusion, the time-dependent solution for stresses and pore pressures considering the mud and formation shale activities are presented. These solutions are the basis of the software, PBORE-3D, which utilizes contemporary programming techniques and can perform analyses of stress/pore pressure, formation failure, mud weight, and mud-salinity design for drilling shale formations. The model is especially useful in the prediction and visualization of time-dependent break-outs created due to inadequate mud weights; as well as time-dependent alteration of the near wellbore stress concentration caused by excessive mud weights leading to lost circulation problems. A case study is presented in this work which demonstrates the straightforward application of the model to challenging drilling conditions.