The physical underpinnings of fibrosarcoma cell dissemination from a tumor in a surrounding collagen-rich matrix are poorly understood. Here we show that a tumor spheroid embedded in a 3D collagen matrix exerts large contractile forces on the matrix before invasion. Cell invasion is accompanied by complex spatially and temporally dependent patterns of cell migration within and at the surface of the spheroids that are fundamentally different from migratory patterns of individual fibrosarcoma cells homogeneously distributed in the same type of matrix. Cells display a continuous transition from a round morphology at the spheroid core, to highly aligned elongated morphology at the spheroid periphery, which depends on both β1-integrin-based cell-matrix adhesion and myosin II/ROCK-based cell contractility. This isotropic-to-anisotropic transition corresponds to a shift in migration, from a slow and unpolarized movement at the core, to a fast, polarized and persistent one at the periphery. Our results also show that the ensuing collective invasion of fibrosarcoma cells is induced by anisotropic contractile stresses exerted on the surrounding matrix.