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This study theoretically and numerically investigates the dynamics of an underwater explosion bubble near a free surface. A refined theoretical model is proposed, based on the potential flow theory, in order to improve its accuracy and extend its range of application to near-field scenarios. Furthermore, the two-dimensional axisymmetric Structured Arbitrary Lagrangian-Eulerian (S-ALE) method implemented in LS-DYNA is utilized to capture the bubble-water interface in numerical simulations. A convergence study is performed on the sizes of mesh and computational domain to reduce computation time while maintaining adequate accuracy in the results. The chosen finite element modeling strategy is validated by the Gilmore model, classical empirical formulas, and a reference experiment. After that, the evolution of the bubble shape is simulated for various values of γ f (the dimensionless distance from the initial bubble centroid to the free surface) and δ (the buoyancy parameter). Observations reveal that the free surface results in a slight increase in the maximum bubble radius, which is quantified as a linear fitting equation to allow a precise determination of the initial bubble radius. By combining the present model, simulations, and literature data, it is found that there are differences in the relationships between the dimensionless bubble oscillation period τ and γ f among UNDEX and cavitation bubbles, as well as among UNDEX bubbles with varying maximum radii. In any case, there is a positive correlation between τ and γ f , while the influence of δ on τ varies depending on the exact value of γ f. Meanwhile, the present model's predictions concerning migration history and collapse position generally match with the simulations and reference data. A reversal in the direction of bubble migration is observed when γ f is very small, which is caused by the substantial dependence of the Bjerknes force on the pressure gradient between the bubble interior and the ambient environment. • The refined theory was fully validated by sophisticated numerical simulations. • A method was proposed to more accurately calculate the initial bubble radius. • The refined theory applies even to bubble very close to a free surface (γ f = 1). • The study showed in detail how γ f and δ affect bubble dynamics. • Differences in behaviors among cavitation and UNDEX bubbles were presented. [ABSTRACT FROM AUTHOR]