The ongoing loss of polar ice masses has placed increased interest in the numerical modeling of ice shelves. In order to adequately describe their mechanical response, a model must account for both instantaneous elastic effects and time-dependent viscous deformation, particularly in the presence of evolving load conditions, see [1]. In this contribution, a finite viscoelastic Maxwell formulation for ice is proposed that consistently captures deformation processes across short and long time scales, see [2]. The model is derived using a multiplicative split of the deformation gradient into elastic and viscous contributions and derived using a Lie derivative. For the temporal discretization of the viscous internal variables, an exponential integration scheme is employed, see [3], which inherently enforces isochoric viscous flow, even in long-term simulations. The classical Maxwell model is further extended to represent the nonlinear creep behavior characteristic of ice by incorporating Glen's flow law, see e.g. [4]. This results in a stress-dependent effective viscosity, enabling a direct coupling between the effective stress state and the viscous deformation rate, while preserving the underlying structure of the exponential update scheme. The applicability of the approach is illustrated by means of ice shelf benchmark problems, with numerical results presented in terms of the temporal evolution of stresses and displacements. [1] J. Christmann, R. Müller, and A. Humbert. On nonlinear strain theory for a viscoelastic material model and its implications for calving of ice shelves. Journal of Glaciology, 65(250):212-224, 2019. [2] J. Schröder, M. Koßler, R. Müller, and A. Humbert. A multiplicative finite viscoelastic model for ice using an exponential update formulation (submitted). 2026. [3] S. Reese and S. Govindjee. A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures, 35(26-27):3455-3482, 1998. [4] K. Cuffey and W.S.B. Paterson. The Physics of Glaciers. Elsevier, 4th edition, 2010.