The Moving Particle Semi-implicit (MPS) method is a meshless method based on the Lagrangian perspective. It effectively avoids mesh distortion when simulating problems with large free-surface deformations, such as water entry and exit of structures, numerical wave generation, and dam breaks. Additionally, its free surface detection algorithm is straightforward and ensures accurate interface tracking, showing broad application prospects. To date, research on numerical wave generation using the MPS method has primarily focused on wave-structure interactions, with relatively limited validation analysis dedicated to the wave generation process itself. To address this gap, this study establishes a two-dimensional numerical wave tank model based on the MPS method, incorporating an improved particle shifting scheme and stabilization operators. Regular waves were generated using a piston-type wavemaker and numerically absorbed in a damping zone. Multiple sets of regular waves with different parameters were simulated to analyze the influence of damping coefficients on the results. Furthermore, the model was validated against experimental motion data of a floating box in waves. The results demonstrate that the proposed model can accurately simulate regular waves with various parameters. The wave amplitude error is positively correlated with the reflected wave energy, and selecting appropriate damping coefficients can effectively minimize the influence of reflected waves on the numerical results. Moreover, the simulated motion time history of the floating box agrees well with the experimental data, confirming the feasibility of the model for solving wave-structure interaction problems.