A double-angle indenter model is proposed to determine the representative strain in the indentation process, and a new method is then developed aiming at the extraction of the yield strength and strain-hardening exponent from the surface layer of metals, because surface properties, especially in a small region, may differ from bulk ones and are sometimes closer to service properties such as fatigue strength, wear, and corrosion resistance. First, the isotropic metal was analyzed, the elastic modulus of which was fixed at 128 GPa, the yield strength was 50 to 200 MPa, and the strain-hardening exponent was 0.1 to 0.5. By introducing the yield strain to substitute the yield strength in the calculation, it was proved that the model can cover the majority of metals because the introduced weight parameter λ is independent of the yield strength and the elastic modulus, although it depends on the strain-hardening exponent to some extent. For the determination of yield strain εY (or yield strength Y), the precision is better for low C/E and low n, whereas for the determination of strain-hardening exponent n, the precision is better for high C/E and low εY. By using the double-angle indenter, the material constitutive relationship at the surface can be evaluated from just one indentation without any other measurements.