The paper presents an elastic–viscous–plastic (EVP) model for sea ice dynamics, which aims to improve the computational efficiency and accuracy of the standard viscous–plastic (VP) model. The VP model treats sea ice as a visco-plastic material, but it suffers from numerical difficulties due to the large viscosities in regions of low strain rates, requiring implicit methods with stringent time step restrictions. The EVP model introduces an elastic component that dominates at short timescales, allowing for explicit numerical schemes. This modification reduces the computational burden and improves the model's performance. The authors develop and test two methods: a preconditioned conjugate gradient method for solving the EVP equations and an explicit elastic-viscous-plastic scheme. The elastic-viscous-plastic model is shown to be more accurate in capturing transient behavior and is computationally more efficient, especially for large time steps. The paper also includes a heuristic analysis and a one-dimensional test problem to validate the EVP model's performance.The paper presents an elastic–viscous–plastic (EVP) model for sea ice dynamics, which aims to improve the computational efficiency and accuracy of the standard viscous–plastic (VP) model. The VP model treats sea ice as a visco-plastic material, but it suffers from numerical difficulties due to the large viscosities in regions of low strain rates, requiring implicit methods with stringent time step restrictions. The EVP model introduces an elastic component that dominates at short timescales, allowing for explicit numerical schemes. This modification reduces the computational burden and improves the model's performance. The authors develop and test two methods: a preconditioned conjugate gradient method for solving the EVP equations and an explicit elastic-viscous-plastic scheme. The elastic-viscous-plastic model is shown to be more accurate in capturing transient behavior and is computationally more efficient, especially for large time steps. The paper also includes a heuristic analysis and a one-dimensional test problem to validate the EVP model's performance.