In this chapter, we discuss how two-way coupled fluid flow and geomechanics can be modeled in the MATLAB Reservoir Simulation Toolbox (MRST) using the ad-mechanics module. A brief introduction to linear poroelasticity is provided, which is a common framework for studying geomechanics in the context of reservoir management or groundwater applications. We review commonly used poroelastic coefficients and moduli and present a handy tool that removes the need to manually navigate the large number of poroelastic relationships to compute values of needed parameters. The chapter further provides three examples where well-known model cases in linear elasticity and poroelasticity are modeled in MRST and compared with results from analytical estimates. These examples include the compression of a dry sample (a linear elastic problem) as well as the compression of a wet sample (Terzaghi’s problem) and Mandel’s problem.