Abstract This work presents a procedure to assess, by an approximate lower bound, the dynamic stress distribution that prevails in the deforming zone during fast forming processes. An objective measure to what is “a fast process” will be determined by the magnitude of three dimensionless groups which characterize dynamic plasticity. The suggested generalization of the lower bound calls for admissible trials of “dynamic stress” solutions for rigid-plastic and, possibly, viscoplastic materials. The analysis becomes a rigorous lower bound as the speed approaches zero. Otherwise, it elevates the true bound with quantified speed-dependent terms associated with the above groups. Applications are demonstrated via examples. Technological limitations imposed by the high speed are indicated. Experimental data and/or numerical solutions are added for comparisons whenever these exist.