In this article we present an analytical method for deriving the relationship between the pressure drop and flow rate in laminar flow regimes, and apply it to the flow of power-law fluids through axially-symmetric corrugated tubes. The method, which is general with regard to fluid and tube shape within certain restrictions, can also be used as a foundation for numerical integration where analytical expressions are hard to obtain due to mathematical or practical complexities. Five converging–diverging geometries are used as examples to illustrate the application of this method.