The side-wall pressure distribution in static silos is an important and open problem related to storage safety of granular materials. Referring to Lvin's theory [Powder Technology 4, 280 (1971)] and Rodolfo's 2D numerical result [Phys. Rev. E 97.1(2018)], a new theoretical model of side-wall pressure is established by assuming the friction coefficient as well as the ratio of horizontal to vertical stress changing with depth position in granular columns. Furthermore, the transition of stress state between hydrostatic-like and Janssen-like in a cylindrical granular container with flat bottom is systematically investigated by our model and experiment, and finally an empirical expression describing this transition is proposed. (C) 2019 Published by Elsevier B.V.