Subroutines RDRAT and PARM3 enable computer programs such as the BRANCH open-channel unsteady-flow model to route flows through or over combinations of critical-flow sections, culverts, bridges, road- overflow sections, fixed spillways, and(or) dams. The subroutines also obstruct upstream flow to simulate operation of flapper-type tide gates. A multiplier can be applied by date and time to simulate varying numbers of tide gates being open or alternative construction scenarios for multiple culverts. The subroutines use three-parameter (headwater, tailwater, and discharge) rating table lookup methods. These tables may be manually prepared using other programs that do step-backwater computations or compute flow through bridges and culverts or over dams. The subroutine, therefore, precludes the necessity of incorporating considerable hydraulic computational code into the client program, and provides complete flexibility for users of the model for routing flow through almost any affixed structure or combination of structures. The subroutines are written in Fortran 77 language, and have minimal exchange of information with the BRANCH model or other possible client programs. The report documents the interpolation methodology, data input requirements, and software.