In this work, a previously proposed finite element is applied in conjunction with a modal approach to predict the lateral buckling resistance of the tensile armors in flexible pipes. The finite element represents the mechanical behavior of tensile armors settled on elastic foundations, which model the frictional interaction between these armors and the surrounding layers. This FE modal approach is used to evaluate the buckling response of 44 different tensile armors considering 15 different friction coefficients between layers. The responses obtained formed a dataset employed in symbolic regression analyses that led to an analytical formulation capable of adequately reproducing the numerical results with minimum computational effort. The results obtained with this analytical formulation are compared to those from other numerical models and experimental measurements showing good agreement and evidencing the potential of the proposed formulation.