Mechanistic analysis is crucial in pavement engineering for predicting how pavements behave under traffic loading. Traditional methods, such as Layered Elastic Theory (LET) and Finite Element Analysis (FEA), are widely used but can become computationally intensive when numerous analyses are required. This paper presents a novel application of Graph Attention Networks (GATs) that demonstrates superior generalization capabilities across varying pavement configurations while maintaining prediction accuracy. By representing pavement systems as graphs, where nodes represent spatial points within layers and edges capture structural relationships, our GAT model effectively learns the underlying physics of strain propagation while eliminating the need for mechanistic pre-analysis. The model's attention mechanism allows it to dynamically focus on critical layer interactions, particularly at boundaries where strain behavior changes significantly. In comparative evaluations, the GAT model achieved mean absolute errors of 1.75, 0.78 and 0.77 for vertical, radial, and tangential strains respectively, outperforming both full-knowledge and partial-knowledge neural networks. Most notably, the model maintains high accuracy when tested on pavement structures with different numbers of layers and material configurations than those used in training, demonstrating robust generalization capabilities. These results establish GATs as a promising tool for mechanistic pavement analysis.