We have developed a new method of analysis to describe the propagation of induced fluid-driven fractures in rock masses which contain pre-existing discontinuities such as joints, faults, bed interfaces, lens boundaries, etc. The analysis is based on a 2-dimensional model, with coupled solid mechanics, fracture mechanics, and fluid mechanics. The solid and fracture mechanics are solved by an implicit finite element approach which provides for mixed-mode (I and 11) fracture propagation in arbitrary stress fields. The fluid mechanics capability first was established for steady-state conditions, using a finite element formulation for flow between parallel surfaces. This initial coupling resulted in the version 1.0 of the FEFFLAP model (Finite Element Fracture and Flow Analysis Program). This version was verified against analytical solutions, and tested for validation against results of hydrofracturing in blocks of rock simulants containing an interface, under biaxial loading, as described in Part 2, the companion paper to this publication.