Metastasis contributes to over 90 percent of cancer mortalities and may be influenced by the extracellular matrix (ECM). ECM microenvironments differ in matrix organization, cell-matrix adhesions, and fiber rigidity, which may affect cancer migration and, thus, should be investigated. To understand the interactions between cancer cells and the ECM, we simulate local invasion through ECM organizations of varying determinants. Randomly curved organizations of normal ovarian stroma exhibit minimal local invasion. In contrast, wave-like and parallel linear structures in reorganized ECM organizations provide contact guidance, which increases cancer invasiveness. ECM organizations with strong cell-matrix attachments generate cell pseudopodia, which aid in increasing invasion rate, while weaker attachments prevent the cells from attaching to the fibers and forming pseudopodia, limiting local invasion. ECM organizations with rigid fibers elongate the cell body, allowing them to form cell protrusions and spread rapidly. Conversely, soft fibers stimulate cell rounding and limit migration. Optimizing cell-matrix adhesions and fiber rigidity results in below 10 percent local invasion and reinforces the importance of using computational modeling to discover novel approaches to restricting cancer movement.