Laser-induced breakdown spectroscopy (LIBS) technology, as an effective tool for material composition analysis, has broad application value. However, due to the poor repeatability of LIBS and the influence of matrix and self-absorption effects, spectral data contains a large number of redundant features that are useless for quantitative analysis. To overcome the difficulty in improving prediction accuracy when using raw full spectrum data as model input, two feature engineering techniques (minimum absolute shrinkage and selection operator regression LASSO and sequential backward selection SBS) were combined with machine learning to achieve a quantitative analysis of nickel (Ni), titanium (Ti), and chromium (Cr) in stainless steel samples. This study used seven stainless steel samples with different element contents purchased from Steel Research Nanogram Testing Technology Co., Ltd. as the research objects. Seventy LIBS spectra were obtained, and four different data preprocessing methods were compared, including Maximum Minimum Normalization (MMN), Standard Normal Variation (SNV), Savitzky Golay Smooth Filtering (SG), and Internal Standard Method (IS). The preprocessing results were detected using Root Mean Square Error (RSME). Finally, Savitzky Golay smoothing filtering was chosen for spectral preprocessing. Effective variables were independently selected for different quantization elements when selecting features using LASSO and SBS algorithms. Then, three different feature combinations, namely full spectrum, LASSO selection feature, and SBS selection feature were used as inputs to the model. To verify the effectiveness of the feature selection method, partial least squares (PLS) Compare two different machine learning models using a Support Vector Machine (SVM). Evaluate the performance of different models using Average Relative Error (ARE) and Relative Standard Deviation (RSD). The results showed that the model inputs selected by the two feature selection methods showed better prediction accuracy and stability compared to full-spectrum inputs in different machine learning models. Among them, the LASSO-PLS model achieved the best prediction accuracy in the quantitative analysis of Ni, Ti, and Cr elements, with ARE of 3.50%, 2.66%, and 0.93%, and RSD of 4.55%, 5.23%, and 2.04%, respectively. Therefore, the LIBS combined with LASSO and SBS algorithms proposed in this article can accurately and stably quantify the Ni, Ti, and Cr elements in stainless steel, providing a reference for further exploring the application of LIBS combined with machine learning in stainless steel element quantification analysis scenarios.