A load vs. displacement model LDM-PS is proposed, and a conical indentation test method for obtaining the stress-strain relationship of the material under the Ramberg-Osgood law (R-O law) is proposed by the grounds of energy density equivalence, considering the proportional superposition of strain energy between linear law pure elasticity and power law pure plasticity in conical indentation. For 80 set materials, the load-displacement curve (forward prediction) predicted by LDM-PS is in a close agreement with the results of Finite Element Analysis (FEA), and the load-displacement curve obtained by FEA is taken as the experimental simulation curve. Two kinds of cone angle conical indenters are used to carry out single conical indentation (double conical indentation) twice on the surface of smooth material, and the R-O law parameters can be solved by parabolic law regression of the two loading vs. displacement curves of double conical indentation at the loading stage. The stress vs. strain curve of R-O law predicted by LDM-PS (inverse prediction) is in a close agreement with the condition curve of FEA. The stress vs. strain relationship, Young's modulus and strength predicted by the new method are in a good agreement with the results of the traditional uniaxial tensile test.