Reinforced concrete (RC) flat slabs, a popular choice in construction due to their flexibility, are susceptible to sudden and brittle punching shear failure. Existing design methods often exhibit significant bias and variability. Accurate estimation of punching shear strength in RC flat slabs is crucial for effective concrete structure design and management. This study introduces a novel computation method, the jellyfish-least square support vector machine (JS-LSSVR) hybrid model, to predict punching shear strength. By combining machine learning (LSSVR) with jellyfish swarm (JS) intelligence, this hybrid model ensures precise and reliable predictions. The model’s development utilizes a real-world experimental data set. Comparison with seven established optimizers, including artificial bee colony (ABC), differential evolution (DE), genetic algorithm (GA), and others, as well as existing machine learning (ML)-based models and design codes, validates the superiority of the JS-LSSVR hybrid model. This innovative approach significantly enhances prediction accuracy, providing valuable support for civil engineers in estimating RC flat slab punching shear strength.