The ice age is both an interesting diagnostic tool and parameter for determining the ice physical properties (albedo, strength, salinity, etc.). There are basically two ways of modelling the ice age: as a bidimensional tracer or as a vertical tracer, but different definitions lead to various interpretations. In this work, we first present the equation of evolution of the age in a one-dimensional ice layer. This equation is applied to a stand-alone thermodynamic sea-ice model and its numerical resolution is compared with the integration of the ice age thanks to Lagrangian particles in the vertical direction. In a second step, a two-dimensional Lagrangian, finite element, adaptive sea-ice model is presented. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. Our model has representations of both dynamic and thermodynamic sea-ice processes and includes viscous–plastic rheology along with a complete parameterization of the atmospheric fluxes. In this Lagrangian version of the model, the computational grid moves with the ice drift. In order to maintain a good quality of the mesh, the mesh has to be adapted during the simulation, involving particular mesh adaptation techniques. A simulation of the Arctic basin is carried out where the Lagrangian model is used to transport the vertical structure of ice age. A comparison with another definition of the ice age (modelled as a bidimensional tracer) is finally analyzed. This Lagrangian model is thought to be particularly well suited to comparison with ice-age estimates of satellite data based on ice tracking.