The present study investigates the vibrational behavior of a circular hinge-less arch with the presence of cracks, focusingon in-plane natural frequencies under varying damage and geometric scenarios. Finite element simulations were conductedusing ANSYS 2020, and results were validated against experimental data using Labshop program. To enhance the predictivecapability of the proposed hybrid FEM-ML model, two supervised learning algorithms viz., support vector regression(SVR) and decision tree (DT) were implemented using the scikit-learn library in Python. The SVR model employed RadialBasis Function (RBF) kernel to capture nonlinear relationships between structural and frequency response. The analysisconsidered the effect of crack depth, crack location, and cross-sectional geometry. It was observed that natural frequencydecreases significantly with increasing crack depth, regardless of its position. Notably, cracks located farther from supportscaused a more pronounced regarding in frequency. Additionally, a change in section radius was found to significantlyinfluence frequency, with a doubling of the radius leading to 74% decrease. To enhance predictive capabilities, machinelearning models viz., Support Vector Regression, and Decision Tree were employed to estimate natural frequencies basedon structural features such as crack depth ratio, position, and section type. The models demonstrated high accuracy,validated using RMSE and MAE metrics. The FEM data were divided into 80% of data were used for training and 20%used for testing with fivefold cross validation applied during testing for hyper parameter optimization. The optimal SVRconfiguration was found at C = 10, ε = 0.01, γ = 0.1, while DT model achieved, its best performance with a maximum depthof 10, minimum sample split of 5. Minimum sample leaf of 2 using mean squared error. A comparison with existingliterature showed a maximum discrepancy of 5.7% in frequency results, confirming the strength of proposed approach.Thus hybrid FEM-ML methodology offers a fast, data-driven, and reliable alternative for structural health monitoring ofdamaged curved beam systems.