Angiogenesis is the process by which new blood vessels sprout from existing vessels, enabling new vascular elements to be added to an existing vasculature network. Mechanical interactions during angiogenesis, i.e., traction forces applied by neovessels and the corresponding deformation of the extracellular matrix (ECM), are important regulators of growth and neovascularization. However, the dynamic relationship between cell-generated forces, the deformation of the ECM, and the topology of the emerging vascular network are poorly understood. The goal of this research was to develop, implement, and validate a computational framework that simulates the dynamic mechanical interaction between angiogenic neovessels and the ECM. This dissertation presents a novel continuous-discrete finite element (FE) model with angiogenic growth coupled with matrix deformation. Angiogenesis was simulated using a discrete growth model. This model uses properties of the ECM, represented by a continuous FE mesh, to regulate angiogenic growth and branching and was capable of accurately predicting vascular morphometric data when simulating growth in various matrix conditions. To couple growth with matrix deformation, sprout forces were applied to the mesh and the corresponding deformation of the matrix was determined using the nonlinear FE software FEBio. This deformation was then used to update the ECM into the current configuration before calculating the next growth step. Data from vascularized gel experiments were used to both calibrate mechanisms within the model during implementation and compare with computational simulations to assess the validity of the simulations. In simulations of experiments involving vascularized collagen gels subjected to various mechanical boundary constraints, this coupled framework accurately predicted gel contraction and microvessel alignment for each condition. The primary mechanism for alignment occurs as microvessels passively align while moving with the deformation of the surrounding matrix. These results demonstrate how biomechanical cellular activity at the microscale during morphogenic processes such as angiogenesis can influence the macroenvironment and induce patterns and organization. These methods provide a flexible computational platform to investigate the mechanisms by which the biomechanical interaction between cells and the ECM regulates the structure and composition of the emerging tissue during morphogenesis.