Abstract The present study is concerned with upset forging of arbitrarily-shaped prismatic blocks which is characterized by three-dimensional deformation with sidewise spread and bulging along thickness. A kinematically admissible velocity field to incorporate the three-dimensional deformation is proposed. From the proposed velocity field the upper-bound load and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out with annealed AISI 1015 steel billets and commercially pure copper billets at room temperature for different frictional conditions and geometrical shapes such as clover and rounded rectangles. The theoretical predictions both in the forging load and the deformed configuration are shown to be in good agreement with the experimental results. Therefore, the proposed method of analysis in this work can be used for the prediction of forging load and deformation in upset forging of arbitrarily-shaped prismatic blocks.