The present technology provides a method of building a tire and a tire building machine. When bonding together longitudinal direction end portions of an outer circumferential side strip-shaped rubber member wrapped around a building drum to form a cylindrical shape, inner circumferential surfaces of projecting parts of the longitudinal direction end portions that project in a drum width direction relative to an inner circumferential side strip-shaped rubber member are supported by a support section, and the inner circumferential surfaces are positioned at a level of an outer circumferential surface of the inner circumferential side strip-shaped rubber member. In this state, the projecting parts are pressed in the drum width direction by a pressing section, and the longitudinal direction end portions are bonded together.