A casing string is augmented with one or more variable flow resistance devices or “vibrating tools” to facilitate advancement of the casing and distribution of the cement in the annulus once the casing is properly positioned. The method includes vibrating the casing string while advancing the casing down the wellbore or while the cement is pumped into the annulus, or both. After the cementing operation is completed, the devices may be drilled out to open the casing string for further operations. The casing string assembly may include a vibrating tool at the end in place of a conventional float shoe or float collar. Multiple vibrating tools can be employed in the casing string, and they may be combined with conventional float shoes and collars. Additionally, vibrating tools in the form of plugs can be pumped down and landed inside the casing string.