We present a new brittle rheology and an accompanying numerical framework for large-scale sea-ice modelling. This rheology is based on a Bingham-Maxwell constitutive model and the Maxwell-Elasto-Brittle (MEB) rheology, the latter of which has previously been used to model sea ice. The key strength of the MEB rheology is its ability to represent the scaling properties of simulated sea-ice deformation in space and time. The new rhe-ology we propose here, which we refer to as the brittle Bingham-Maxwell rheology (BBM), represents a further evolution of the MEB rheology. It is developed to address two main shortcomings of the MEB rheology we were unable to address in our implementation of it: excessive thickening of the ice in model runs longer than about one winter and a relatively high computational cost. In the BBM rheology and framework these shortcomings are addressed by demanding that the ice deforms under convergence in a purely elastic manner when internal stresses lie below a given compressive threshold, and by introducing an explicit scheme to solve the ice momentum equation. In this paper we introduce the new rheology and numerical framework. Using an implementation of BBM in version two of the neXtSIM sea-ice model (neXtSIMv2), we show that it gives reasonable long term evolution of the Arctic sea-ice cover and very good deformation fields and statistics compared to satellite observations. Plain Language Summary Sea ice movement is determined by the wind and ocean currents acting on it, and how the ice itself reacts to these forces. In a sea-ice model this reaction is simulated with equations collectively referred to as a rheology. In this paper we introduce a new rhe-ology, called the brittle Bingham-Maxwell (BBM) rheology, and a method for solving the equations on a computer. This new rheology extends the Maxwell-Elasto-Brittle (MEB) rheology we used in previous versions of our sea-ice model, neXtSIM. We used MEB in neXtSIM because this rheology gives a very good description of how the ice reacts to winds and currents, but we found two main faults with it we couldn’t fix: the ice in the model would pile up to become unrealistically thick after several model years, and the model required too much computer time to run. In the BBM rheology we add an extra term to the MEB equations to prevent the excessive piling up of ice, and we also propose a more efficient way to solve the equations. Like its predecessor, the new rheology also allows our model to simulate very well the way the ice moves on daily basis, when compared to satellite observations.