Concurrent growth of multiple fractures in brittle rock is a complex process due to mechanical interaction effects. Fractures can amplify or shield stress on other fracture tips, and stress field perturbations change continuously during fracture growth. A three-dimensional, finite-element based, quasi-static growth algorithm is validated for mixed mode fracture growth in linear elastic media, and is used to investigate concurrent fracture growth in arrays and networks. Growth is governed by fracture tip stress intensity factors, which quantify the energy contributing to fracture extension, and are validated against analytical solutions for fractures under compression and tension, demonstrating that growth is accurate even in coarsely meshed domains. Isolated fracture geometries are compared to wing cracks grown in experiments on brittle media. A novel formulation of a Paris-type extension criterion is introduced to handle concurrent fracture growth. Fracture and volume-based growth rate exponents are shown to modify fracture interaction patterns. A geomechanical discrete fracture network is generated and examined during its growth, whose properties are the direct result of the imposed anisotropic stress field and mutual fracture interaction. Two-dimensional cut-plane views of the network demonstrate how fractures would appear in outcrops, and show the variability in fracture traces arising during interaction and growth.