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Contact guidance is a powerful topographical cue that induces persistent directional cell migration. Healthy tissue stroma is characterized by a meshwork of wavy extracellular matrix (ECM) fiber bundles, whereas metastasis-prone stroma exhibit less wavy, more linear fibers. The latter topography correlates with poor prognosis, whereas more wavy bundles correlate with benign tumors. We designed nanotopographic ECM-coated substrates that mimic collagen fibril waveforms seen in tumors and healthy tissues to determine how these nanotopographies may regulate cancer cell polarization and migration machineries. Cell polarization and directional migration were inhibited by fibril-like wave substrates above a threshold amplitude. Although polarity signals and actin nucleation factors were required for polarization and migration on low-amplitude wave substrates, they did not localize to cell leading edges. Instead, these factors localized to wave peaks, creating multiple “cryptic leading edges” within cells. On high-amplitude wave substrates, retrograde flow from large cryptic leading edges depolarized stress fibers and focal adhesions and inhibited cell migration. On low-amplitude wave substrates, actomyosin contractility overrode the small cryptic leading edges and drove stress fiber and focal adhesion orientation along the wave axis to mediate directional migration. Cancer cells of different intrinsic contractility depolarized at different wave amplitudes, and cell polarization response to wavy substrates could be tuned by manipulating contractility. We propose that ECM fibril waveforms with sufficiently high amplitude around tumors may serve as “cell polarization barriers,” decreasing directional migration of tumor cells, which could be overcome by up-regulation of tumor cell contractility.