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Floating marine debris (FMD) is a pervasive problem in marginal seas worldwide. Driven by the nearshore waves, the FMD gradually accumulates shoreward and has a large chance of being beached, posing a direct threat to the coastal environment. Thus, investigating the nearshore drifting and beaching process of the FMD is of paramount importance. In this article, the trajectories of the FMD on a sloping beach are simulated by the Smoothed Particle Hydrodynamics (SPH) method, which is pre-verified through laboratory experiments. A series of sensitivity tests are conducted numerically on the influence of attributes of FMD as well as varied wave height (H 0), and wave period (T 0) on its beaching process. It is found that the beaching process of the FMD can be divided into three steps: drifting in front of surf zones, surfing and leaping with plunging waves, and advancing via wave runup. The density of the FMD combined with wave steepness determines whether the FMD can enter into the surf zone where it has a large chance to beach. Finally, this article proposed a semi-analytical model with improved Morison's equations considering the second-order Lagrangian transport on a sloping beach. This semi-analytical model is much faster and is comparable in computational accuracy to the high-resolution SPH model. It has the potential to be incorporated into the existing marine models and replace the stochastic process assumed for the FMD's tracking in the nearshore, in order to achieve more accurate assessment on the stranded FMD. [Display omitted] • Beaching process of floating marine debris is simulated by SPH method. • Beaching process is divided into three steps: drift, surf and leap, and translation. • Debris properties and offshore wave conditions codetermine whether debris beach. • Morison's equation is improved to predict debris trajectory before wave breaks. [ABSTRACT FROM AUTHOR]