The paper presents an elastic–viscous–plastic (EVP) model for sea ice dynamics, which improves upon the standard viscous–plastic (VP) model by incorporating elastic behavior. The VP model, while widely used, has numerical challenges due to its large range of viscosities and requires implicit methods for stability, which are computationally expensive. The authors developed two methods to address these issues: a preconditioned conjugate gradient method for solving the VP equations and a modified model that uses an elastic wave mechanism for short timescales, allowing for a fully explicit scheme. This modification improves computational efficiency and accuracy for short timescales associated with wind forcing, while reproducing VP behavior on longer timescales. The EVP model is more accurate for short timescales and computationally more efficient than the VP model. It avoids the complexities of earlier elastic–plastic models by using elastic behavior for numerical efficiency rather than physical realism. The model is also more suitable for parallel computation, as it allows for explicit time-stepping with larger time steps. The authors compare the EVP and VP models using a one-dimensional test problem and show that the EVP model provides more accurate results for short timescales and is computationally more efficient. The model is designed to be compatible with the Parallel Ocean Program (POP) for use in global climate models. The EVP model is validated against numerical results and is shown to produce accurate solutions for both short and long timescales.The paper presents an elastic–viscous–plastic (EVP) model for sea ice dynamics, which improves upon the standard viscous–plastic (VP) model by incorporating elastic behavior. The VP model, while widely used, has numerical challenges due to its large range of viscosities and requires implicit methods for stability, which are computationally expensive. The authors developed two methods to address these issues: a preconditioned conjugate gradient method for solving the VP equations and a modified model that uses an elastic wave mechanism for short timescales, allowing for a fully explicit scheme. This modification improves computational efficiency and accuracy for short timescales associated with wind forcing, while reproducing VP behavior on longer timescales. The EVP model is more accurate for short timescales and computationally more efficient than the VP model. It avoids the complexities of earlier elastic–plastic models by using elastic behavior for numerical efficiency rather than physical realism. The model is also more suitable for parallel computation, as it allows for explicit time-stepping with larger time steps. The authors compare the EVP and VP models using a one-dimensional test problem and show that the EVP model provides more accurate results for short timescales and is computationally more efficient. The model is designed to be compatible with the Parallel Ocean Program (POP) for use in global climate models. The EVP model is validated against numerical results and is shown to produce accurate solutions for both short and long timescales.