Wellbore stability problems are most common when drilling through shales. In order to avoid such problems in this kind of rocks the solute concentration and temperature must be properly defined in the drilling fluid composition, which requires considering poroelastic, thermal and chemical effects in a coupled way. The equations complexity of coupled models usually results in numerical solutions that are very time consuming, thus, unattractive for stability analysis. In an opposite way, it is very difficult to develop closed- form solutions for coupled models. This work presents a thermochemoporoelastic model represented by a numerical solution based upon the finite element method and an analytical solution based upon the Laplace transform method. A comparison between the results of the numerical solution and analytical solution shows that the later can reproduce the coupled processes involved in the wellbore stability problem in shales as well as the former, and for this reason the closed-form solution can be applied as a practical tool in wellbore stability analysis. The analysis of a typical wellbore drilled through shales showed that an efficient control of wellbore stability can be obtained through an adequate specification of the drilling fluid pressure when taking in account its solute concentration and temperature. The model was also able to explain some problems not predicted by uncoupled models, but almost always seen while drilling through shales.