We present a simple and efficient implementation of a viscous creep rheology based on diffusion creep, dislocation creep, and the Peierls mechanism in conjunction with an elasto-plastic rheology model into a shock-physics code, the iSALE impact code. Our approach is based on the calculation of an "effective viscosity" which is then used as a reference viscosity for any underlying viscoelastic (or even visco-elasto-plastic) model. Here we use a Maxwell-model which best describes stress relaxation and is therefore likely most important for the formation of large meteorite impact basins. While common viscoelastic behavior during mantle convection or other slow geodynamic or geological processes is mostly controlled by diffusion and dislocation creep, we show that the Peierls mechanism dominates at the large strain rates that typically occur during meteorite impacts. Thus, the resulting visco-elasto-plastic rheology allows implementation of a more realistic mantle behavior in computer simulations, especially for those dealing with large meteorite impacts. The approach shown here opens the way to more faithful simulations of large impact basin formation, especially in elucidating the physics behind the formation of the external fault rings characteristic of large lunar basins. K E Y W O R D S hydrocodes, impact cratering, iSALE, visco-elasto-plastic rheology 1 INTRODUCTION The viscoelastic behavior of material has been studied intensively over the last decades. Studies range from engineering and industrial applications, 1-4 as well as biological, 5,6 medical, 7-9 and geological objectives. 10-14 The concept of viscoelasticity was first proposed by Maxwell in 1867. 15 Later on, progress in the understanding of crystal structures of geological † Prior to formal acceptance of this article for publication, the corresponding author Prof. Melosh sadly passed away on 11 September 2020. Despite our best attempts, we have not been able to reach Dirk Elbeshausen for his final approval of the article and we understand that he is no longer in active research but was involved in writing earlier versions of the article.