The use of columns with box sections in the structure of steel buildings with rigid connections is very popular. In these buildings, the bending moment in the rigid connections causes big deformations in the column face. These deformations not only reduce the rigidity of connections but also in the most cases control the design of columns. Then it is necessary to evaluate the values of these deformations accurately. In this research by using the finite element method and Ansys software, the different models of moment frames with rigid connection of beam to box column are studied and the effects of parameters such as: thickness of column face, dimensions of beam and column section, existence of internal stiffeners etc. on the value of column face deformation are investigated. Finally, appropriate graphs and formula are presented to calculate the box column face deformation and for using in structural design. Also applicable and administrative methods for reduction of theses deformations are proposed.