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On small-meso scale, the sea ice dynamic characteristics are quite different from that on large scale. To model the sea ice dynamics on small-meso scale, a new elastic-viscous-plastic (EVP) constitutive model and a hybrid Lagrangian- Eulerian (HLE) numerical method are developed based on continuum theory. While a modified discrete element model (DEM) is introduced to model the ice cover at discrete state. With the EVP constitutive model, the numerical simulation for ice ridging in an idealized rectangular basin is carried out and the results are comparable with the analytical solution of jam theory. Adopting the HLE numerical model, the sea ice dynamic process is simulated in a vortex wind field. The furthering application of DEM is discussed in details for modeling the discrete distribution of sea ice. With this study, the mechanical and numerical models for sea ice dynamics can be improved with high precision and computational efficiency.