This study aims to investigate the mechanical behavior of cement mortar and concrete through a hybrid approach that integrates artificial intelligence (AI) techniques with finite element modeling (FEM). Support Vector Machine (SVM) models with Radial Basis Function (RBF) and polynomial kernels, along with Multilayer Perceptron (MLP) neural networks, were employed to predict the compressive strength (Fc) and flexural strength (Fs) of cement mortar incorporating nano-silica (NS) and micro-silica (MS). The dataset comprises 89 samples characterized by six input parameters: water-to-cement ratio (W/C), sand-to-cement ratio (S/C), nano-silica-to-cement ratio (NS/C), micro-silica-to-cement ratio (MS/C), and curing age. Simultaneously, the axial compressive behavior of C20-grade concrete was numerically simulated using the Concrete Damage Plasticity (CDP) model in ABAQUS, with stress–strain responses benchmarked against the analytical models proposed by Mander, Hognestad, and Kent–Park. Due to the inherent limitations of the finite element software, it was not possible to define material models incorporating NS and MS; therefore, the simulations were conducted using the mechanical properties of conventional concrete. The SVM-RBF model demonstrated the highest predictive accuracy with RMSE values of 0.163 (R² = 0.993) for Fs and 0.422 (R² = 0.999) for Fc, while the Mander model showed the best agreement with experimental results among the FEM approaches. The study demonstrates that both the SVM-RBF and CDP-based modeling approaches serve as robust and complementary tools for accurately predicting the mechanical performance of cementitious composites. Furthermore, this research addresses the limitations of conventional FEM in capturing the effects of NS and MS, as well as the existing gap in integrated AI-FEM frameworks for blended cement mortars.