Triply periodic minimal surface (TPMS) lattices have emerged as promising architectural materials for lightweight structural, thermal, and biomedical applications owing to their smooth curvature, tunable relative density, and favorable manufacturability. However, predicting their elastic behavior remains challenging, especially for stochastic variants in which geometric irregularities introduce nonlinear structure–property relationships. This study developed a systematic machine-learning framework to predict the isotropic elastic constants of stochastic gyroid-based TPMS lattices. A dataset was constructed by varying the unit-cell size, relative density, architecture type (sheet or solid), and surface area, with homogenized elastic properties extracted from the stiffness and compliance matrices based on the isotropic assumption. The Random Forest (RF) and Bayesian Ridge Regression (BRR) models were evaluated using an 80/20 training–test split. For stiffness-related properties, the RF model achieved a coefficient of determination (R²) value of 0.85 for the elastic modulus E, 0.92 for the shear modulus G, 0.86 for the bulk modulus K, and strong performance for the anisotropy index (AU) (R² = 0.80), demonstrating its ability to capture nonlinear geometric behavior. The BRR model provided superior accuracy for E, G, K, Poisson’s ratio, and Zener’s ratio and offered interpretable linear coefficients. However, the BRR failed to capture the AU. These two models provide complementary benefits: RF excels in predictive fidelity, whereas BRR enables equation-based design insights. The framework establishes a fast, accurate, and interpretable approach to predict TPMS elasticity and supports future work that integrates experimental validation using additively manufactured polyethylene terephthalate glycol samples and a neural-network-based inverse design.