The goal of this work was the development and evaluation of an algorithm for the approximation and automatic subtraction of continuum backgrounds in laser-induced breakdown and Raman spectra. The background correction algorithm was applied to simple and complex spectra and its effect on identification accuracy was studied. Linear correlation was used for the identification of plastic samples using both laser-induced breakdown and Raman spectra. For both techniques, the algorithm successfully eliminated continuum background without compromising spectral integrity. A significant improvement in the percentage of correct plastic identifications was observed for Raman spectra. The approach should be applicable to a wide range of background correction problems in atomic and molecular spectroscopy.