The plastic strain in a specimen introduced by compression with a pair of anvils is evaluated using a three-dimensional dynamic finite element analysis. The stress-strain relations depending on strain rate and temperature are used in the analysis. The contact condition between the anvil and the specimen is determined from the experimental result from an identically deformed screw set in the specimen. The plastic strain introduced by uni-direction compression is compared with that by bi-direction compression simultaneously or non-simultaneously given from different directions. The non-simultaneous bi-direction deformation is proposed as a method to introduce a large plastic strain widely in the specimen. The bi-direction deformation can be developed as a technique to obtain ultra-fine grain steels for thick plates.