The aim of the research has been to formulate models capable of representing stationary and propagative material instabilities, with special attention paid to strain-rate dependence of the results. In the work large strain plasticity models have been used with optional thermo-mechanical coupling. Viscosity and/or higher order gradients have been included. In the first part of the paper, stationary instabilities are simulated for a plate in tension. Next, the simulations of Lueders bands in tension and shear are presented. In the third part, the simulation results for the Portevin-Le Chatelier (PLC) effect are considered. For this purpose, the computation models are enriched with the Estrin-MacCormick component describing strain rate softening. The simulations for a bone-shape sample in tension are compared with published experiments. Finally, the simulations of new laboratory experiments carried out at TU Dortmund are presented. The examination of aluminum alloy AW5083 shows at the beginning Lueders bands and then saturation hardening with serrations characteristic for the PLC effect. Parametric studies are performed at every stage of the work. The developed models are able to reproduce instabilities taking into account strain-rate dependence. A good agreement between experiments and computations is achieved. The research results are published in [1, 2, 3, 4, 5]. REFERENCES [1] M. Mucha, B. Wcislo, and J. Pamin. Instabilities in membrane tension: Parametric study for large strain thermoplasticity. Arch. Civ. Mech. Eng., 18, 1055-1067, 2018. [2] M. Mucha, B. Wcislo, and J. Pamin. Simulation of a propagative instability in shear using gradient-enhanced and viscoplastic model. Computer Methods in Materials Science, 19, 57-63, 2019. [3] M. Mucha, B. Wcislo, and J. Pamin. Simulation of Lueders bands using regularized large strain elasto-plasticity. Arch. Mech., 73, 83-117, 2021. [4] M. Mucha, B. Wcislo, and J. Pamin. Simulation of PLC effect using regularized large strain elasto-plasticity. Materials, 12, 1-21, 2022. [5] M. Mucha, L. Rose, B. Wcislo, A. Menzel, and J. Pamin. Experiments and numerical simulations of Lueders bands and Portevin-Le Chatelier effect in aluminium alloy AW5083. Arch. Mech., 75, 301-336, 2023.