Local elastic roll flattening in direction of the roll axis in flat ro
lling is one of the important displacement components related to the r
oll gap shape. Up to now some classical formulae to solve roll flatten
ing have been proposed. These formulae were derived from the elastic h
alf space theory or the 2-dimensional contact theory. On calculating t
he flattening of the back-up roll they may result in a great deviation
. In the present effort a comparison was made between the flattening r
esults obtained by a 3-dimensional finite element method and by a clas
sical formula. The relation between the deviation and the back-up roll
geometry was also examined and therefore the classical formula was mo
dified. Calculated results indicate that the modified formula can more
accurately predict the back-up roll flattening.