A quasi-steady elastic-plastic sea ice dynamics model is introduced for long-term simulations. Tidal and inertial oscillations are removed by discarding the negligible inertia term. With this assumption the model is integrated using an implicit numerical scheme. Results are shown for a one-dimensional case. This approach eliminates the elastic waves that typically contaminate elastic-plastic simulations and allows the elastic-plastic constitutive law to be integrated over longer time periods, with the potential for being used effectively for climate dynamics studies. ¿ 2001 American Geophysical Union