Fractures prevail mechanical behavior of a rock mass and confer an overall anisotropic response. Engineering analyses in the elastic regime often use transverse isotropy to model fractured rock masses with a single fracture set. An alternative implicit joint-continuum model combines the mechanical response of the intact rock and fractures by adding their compliance matrices. It can accommodate multiple fracture sets and non-linear fracture response. While the transverse isotropic model is inadequate to model fractured rock media because of its inherent assumptions on the continuity for all stress components, the implicit joint-continuum model is verified against the exact solutions of internal stress distributions and displacement field. The analysis of strip foundations using the implicit joint continuum approach shows that the maximum settlement and tilt will take place when the fracture set strikes quasi-collinear with the strip direction (θJ ≈ ±15°) and the fracture dip angle is either βJ ≈ 40° ± 10° or βJ ≈ 140° ± 10°.