Randomness in material parameters lead to uncertainties in the material response. In engineering simulations, accurate uncertainty quantification is usually associated with high computational cost. Time-separated Stochastic Mechanics (TSM) [1] allows for the efficient inclusion of stochasticity in numerical simulations by separating the time-independent and stochastic variables from the time-dependent and deterministic basis. We extend the TSM approach to the simulation of viscoelastic material behavior under finite strain. For the simulation of structures, the finite element method is incorporated. The extension is based on a constraint-conforming material model for finite-strain viscoelasticity which is derived using the procedure presented in [2]. It allows the algorithmic treatment with implicit Euler time integration by incorporating the viscous volume-preserving constraint through a Lagrange multiplier. The numerical results obtained by the TSM approach are compared to those of the Monte Carlo method and confirm the accuracy and numerical efficiency of TSM. References [1] H. Geisler, C. Erdogan, J. Nagel and P. Junker. ”A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics”. In: Computational Mechanics (2024). [2] T. Bode, M. Soleimani, C. Erdogan, K. Hackl, P. Wriggers and P. Junker. ”On constraint-conforming numerical discretizations in constitutive material modeling”. In: Computational Mechanics (2024).