Tree-like networks form the basic architecture for many organs in the body. In the developing embryo, these structures are shaped by a process known as branching morphogenesis, in which a simple epithelial tube is sculpted into a ramified network via a sequence of iterative branching events. Various chemical signaling mechanisms have been implicated, but in the embryonic lung mechanical forces have also been shown to regulate airway branching morphogenesis. However, how these chemical and physical mechanisms coordinate together to sculpt the functional form of lung is still unclear. This has predominantly been because of the highly interdisciplinary nature of the problem and lack of tools and methods to probe the effect of mechanics on tissue growth. One of the ways to probe tissue mechanics is by estimating patterns of mechanical stresses around the tissue. Many different methods have been developed in past two decades for quantifying mechanical stresses, but most are limited to 2D cellular level experiments. Furthermore, majority of these studies assume the underlying material to have a linear response to deformations generated by cells. Biological systems however, especially during lung development exhibit large deformations and material response can become highly non-linear. This dissertation attempts to bridge this gap by creating a Traction Force Microscopy (TFM) pipeline towards estimating patterns of mechanical stresses around branching embryonic epithelia in 3D matrices. To this end, we used mesenchyme free culture assay which has been previously used to study branching morphogenesis of embryonic lung tissues. We then modified this assay for ex vivo culture of isolated embryonic airway epithelial explants by suspending fluorescent microspheres within the surrounding gel. We demonstrate that these beads can be tracked over the course of many hours to generate a spatial deformation field. Using bead tracking data, we show that there is significant inward (towards epithelium) gel movement during events of epithelial branching suggestive of ECM remodeling near epithelium surface. We also used this tracking data to compute spatiotemporal patterns of strain and stress. Mechanical stress computation however requires knowledge of the mechanical properties of underlying substrate and existing data on the mechanical properties of Matrigel are highly inconsistent and limited to linear small-strain measurements. We thus performed multi-axial deformation mechanical testing of Matrigel to characterize the finite-deformation behavior of this extracellular matrix (ECM) material. These mechanical tests were then combined with quantitative measurements of the deformation fields around cultured embryonic airway epithelial explants to estimate the mechanical stresses exerted during airway branching.