Naturally fractured reservoirs can be treated as dual-porosity media consisting of a primary rock matrix system as well as fractures. These dual-porosity formulations coupling matrix and fracture deformations as well as fluid flow in both systems are first presented. The finite element solution for any directional wellbore drilled in a dual-porosity medium is given. Mud weight considerations are presented for both permeable and impermeable boundary conditions. A case study for inclined wellbore problems was also conducted. The effects of single- and dual-porosity, time, and mud weight are parametrically studied allowing for a better understanding of the physical characteristics governing borehole problems.