A finite-element-based simulation technique is developed in Chapter 1 to predict arbitrary shape evolution of 3-D, geometrically explicit cracks under stable growth conditions. Point-by-point extensions along a crack front are predicted using a new, energy-based growth formulation that relies on a first-order expansion of the energy release rate. The key term in this expansion is the variation of energy release rate, made readily available via the virtual crack extension (VCE) method. The variation of energy release rate acts as an influence function relating changes in applied load to geometry changes along the crack front. The crack-growth formulation is incorporated into an incremental-iterative solution procedure that continually updates the crack configuration by re-meshing. The numerical technique allows crack shapes to evolve according to energy-based mechanics, while reducing the effects of computational artifacts, e.g. mesh bias. Chapter 1 offers three simulations of mode I, planar crack growth as proof-of-concept of the new technique. To extend the simulation approach to more general crack growth situations, Chapter 2 presents a new implementation for decomposing 3-D mixed-mode energy release rates using the VCE method. The technique uses a symmetric/anti-symmetric approach to decompose local crack-front displacements that are substituted into the global VCE energy release rate form. The subsequent expansion leads to the mixedmode energy release rate expressions. As a result of the expansion, previously unaddressed modal-interaction coupling terms are found to impact the mixed-mode energy release rates. Five numerical examples are presented as verification of the implementation. This development expands the VCE method's advantages over similar procedures when simulating arbitrary crack growth. The energy-based growth formulation and accompanying simulation technique is generalized in Chapter 3 to predict arbitrary, mixed-mode, non-planar crack evolution. The implementation uses a novel basis-function approach to generate a crack extension expression, rather than relying on the local, point-by-point approach described in Chapter 1. The basis-function expression dampens the effect of numerical noise on crack growth predictions that could otherwise produce unstable simulation results. Two simulations are presented to demonstrate the technique's ability to capture both general non-planar behavior, as well as local mixed-mode phenomena, e.g. "factory-roof" formation, along the crack front.