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The three parameter Ramberg-Osgood (RO) method finds popular usage for extracting complete stress-strain curve from limited data which is usually available. The currently popular practice of assuming the plasticity to set in only at the Yield point provides computational advantage by separating the complete nonlinear curve, obtained from RO method, into elastic and plastic regions. It is shown, with an example problem, that serious errors are committed by using this method if one compares the obtained results with results of complete stress-strain curve. In the present work we propose a simple Taylor series based approach based on RO method to overcome the above deficiency. This method is found to be computationally efficient. The proposed method is applicable for stress-strain curves of materials for which RO method provides a good approximation.