Cells of all tissue types create and respond to mechanical signals in and from their surrounding extracellular matrix, respectively. However, only recently have the dynamics of this interplay been brought to the forefront of the scientific community’s focus. The surprising finding of this effort, as it pertains to cancer, has been that cell-matrix interactions appear to be at least as critical to understanding the genesis and progression of the disease as are genetics or DNA mutation. The most immediately studied mechanical properties of the extracellular matrix include: the density of the matrix, alignment of the matrix fibers, stiffness of the fibers, and the tension on the fibers. The methods developed for controlling these variables have been numerous, however, few have succeeded in the deconvolution of the set. Here, novel experimentation, device construction, and theoretical treatments aimed to achieve this purpose are presented. The aggregate results of this dissertation argue that while these properties, which have historically been treated as separate mechanical cues in which a cancer cell must contend during invasion, are better interpreted through the single physical lens of energy expenditure. The conclusion is that cancer cells preferentially invade via the energy minimizing path and as such, can be at least partially inhibited by targeting the cells’ external environment rather than exclusively its internal workings as has been the historical approach.