When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from neighbouring cells, degrade the basement membrane, and migrate through the extracellular matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix adhesion. In this paper we present a mathematical model of an intracellular pathway for the interactions between a cancer cell and the extracellular matrix. Cancer cells use similar mechanisms as with normal cells for their interactions with the extracellular matrix. We develop a model of cell-matrix adhesion that accounts for reactions between the cell surface receptor integrins, the matrix glycoprotein fibronectin, and the actin filaments in the cytoskeleton. Each represents components for an intermediate compartment, the extracellular compartment, and the intracellular compartment, respectively. Binding of fibronectin with integrins triggers a clustering of protein complexes, which then activates and phosphorylates regulatory proteins that are involved in actin reorganisation causing actin polymerization and stress fibre assembly. Rearrangement of actin filaments with integrin/fibronectin complexes near adhesion sites and interaction with fibrillar fibronectin produces the force necessary for cell migration, accounting for cell-matrix adhesion.