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Finite Element Analysis (FEA) faces computational challenges when analyzing nonlinear and heterogeneous materials. Utilizing the Mechanical MNIST dataset, comprising 60,000 simulated samples of 28x28 pixel domains under large deformation, the study evaluates classical regression methods (Linear Regression, Random Forest, Gradient Boosting) and advanced deep learning architectures (Convolutional Neural Networks (CNN) and Residual Networks (ResNet)). CNN models achieved superior performance, with a Mean Squared Error (MSE) of 4.21 and an R2 value of approximately 0.982, outperforming classical regression models and slightly surpassing ResNet architectures. These deep learning methods automatically learn spatial relationships from pixel-based representations, eliminating the need for manual feature extraction. The results establish deep learning as a highly effective surrogate modeling technique, enabling rapid and accurate prediction of strain energy compared to conventional FEA methods. This research advances the field towards real-time mechanical predictions, significantly reducing computational expenses in iterative design, optimization tasks, and large-scale simulations.