To determine the pure bond strength between substrate and its overlayed concrete material, a direct pull-off test method was introduced by using a bi-material cylinder with which a penny-shaped crack was mountained at its interface. First, to evaluate the stress magnification or concentration at the interface, the energy release rates of a penny-shaped interface crack in remote tension loading on a bi-material cylinder were determined in terms of different modulus ratios and undonded area ratios(crack ratios) using a commercial finite element program. Then the energy release rates were calibrated as non-dimensional values in consideration of structural dimensions and applied forces. And to evaluate whether this new pull-off test method gives sound test results, three different sizes of unbended area ratios were incorporated along their interface in bi-material cylinders(sulphur polymer concrete + old concrete). Test results showed that all specimens were broken off at their interfaces as intended. Also the FEM analyses and test results indicated that a bi-material specimen with unbended area ratio of 0.4$sim$0.6 is suitable for best accurate testing.