The capability of sparse regression with Least Absolute Shrinkage and Selection Operator (LASSO) in modal identification of a simple system and predicting system response is remarkable. However, it has limitations when applied to more complex structure, particularly in equation discovery and response prediction. Despite these challenges, sparse regression demonstrates superior performance in linear system identification compared to Natural Excitation Technique (NExT) coupled with Eigensystem Realization Algorithm (ERA), especially in identifying higher modes and estimating damping ratios with reduced error.Findings indicate that while sparse regression is highly effective for simple systems, its application to real-world structures requires further exploration. The thesis concludes with recommendations for practical validation of sparse regression on actual structures and its comparison with alternative methods to assess its real-world efficacy in structural health monitoring.