An iterative and incremental procedure for extending linear elastic thermal‐shock vibrational solutions into the plastic region of elastoplastic materials is shown for beams. Only solutions to linear equations of motion are required. Nonlinearity is shifted into a fictitious “temperature‐moment” loading in complete analogy to the temperature loading itself. The problem of thermally induced vibrations in beams is extended to a yielding beam that in the initial state is preloaded statically in pure bending. Thermal shock is considered with nonlinear and (approximate) linear temperature distribution.