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An eddy-current-based SQUID-NDE system has been developed to detect shallow surface flaws of less than 50 mum in depth on heat-exchanger copper tubes using an HTS-SQUID gradiometer and an Helmholtz-coil-type inducer. In this study, detectable flaw sizes on the tubes were investigated by experiments and simulation. Copper tube specimens with flaws of various sizes were inspected by the system with an excitation field of 5.6 muT at 3 kHz. A magnetic anomaly due to the shallowest flaw of 10 mum depth, 100 mum width and 15 mm length was successfully detected. The experimental results showed that the magnetic signal amplitude due to a flaw was proportional to the effective flaw size given by the product of flaw depth, width and length. A numerical simulation was carried out to calculate the magnetic signal from a flaw on a copper tube to determine the dependence on the flaw size. It is concluded that a flaw with a volume of 106 mum3 should be detectable by improving the system parameters.