The thermoviscoelastic dynamic response of a simply supported rectangular steel plate under laser processing is studied in this paper. Three-dimensional transient temperature field of the laser processing thermoviscoelastic rectangular steel plate is solved by the method of separation of variables. Meanwhile, based on von Karman nonlinear strain-displacement relationships and classical thin plate theory, a list of nonlinear dynamic equilibrium equations for a rectangular thermoviscoelastic steel plate are deduced. Then the entire problem is solved by utilizing the Newmark method and the iterative method. Finally, numerical results show that laser moving speed, laser power density and thickness-to-length ratio have a great influence on the thermoviscoelastic response of the rectangular DP980 steel plate. (C) 2016 Elsevier Ltd. All rights reserved.