Laminated composite plates and shells are widely used in aerospace, marine, and automotive industries. Their structural response can be tuned by modifying the stacking sequence, but accurate modelling requires computationally expensive finite element (FE) analysis. This study develops machine learning-based predictive models as surrogates for FE analysis to predict the first natural frequency of laminated composites. Two problems are considered, a 2-variable low-dimensional (LD) problem and a 16-variable high-dimensional (HD) problem. Six machine learning models were trained and evaluated. For the LD problem, support vector regression (SVR) performed best (R² = 0.9972, MSE = 0.0097). For the HD problem, Gaussian process regression (GPR) outperformed others (R² = 1.000, MSE ≪ 0.0001), effectively handling complex nonlinearities. The results highlight SVR’s suitability for simpler cases and GPR’s superior predictive accuracy for high-dimensional design spaces.