<p>This paper is devoted to the study of sloshing waves in the two-dimensional rectangular tanks using a meshless method based on radial basis functions. To enhance numerical stability and computational efficiency, a specialized finite difference formula is proposed for calculating the time derivative of the field function within a coordinate system fixed to the tank. Various simulation scenarios are analyzed to investigate free surface motion and hydrodynamic pressure, including a horizontally excited tank, a standing wave in a stationary tank, a vertically excited tank, and a tank subjected to both vertical and horizontal excitations. Comparisons of the computed results with other available results confirm that the numerical results are in good agreement with the available results in resonance and off-resonance for linear and nonlinear cases. A small discrepancy between the computed results and other available results is observed for cases in which the amplitude and frequency of exciting force are large and approximately equal to the first-order natural frequency of the tank, respectively. This discrepancy may be attributed to the resonant sloshing phenomena, which leads to nonlinear resonant amplification of harmonics.</p>