One of the principal requirements for municipal water distribution systems (WDSs) is to supply water at adequate flow rates and pressures for controlling fires. Guidelines in North America, like the AWWA M32 Manual, define the Available fire flow at a junction to be the maximum flow rate available at a specified pressure (typically in the range of 20psi or 140kPa), considering some network hydraulic constraints (e.g., minimum pressure in the network, or maximum flow velocity in the pipes). Typical demand driven WDSs models, like EPANET, solve the analogous problem of computing the resulting pressure given a specified nodal demand. Therefore, the computation of available fire flows requires iterative runs of demand driven WDSs models. This article compares a number of methods to perform the computation of the available fire flow at the junctions and proposes a new method to make the computation more efficient. The proposed method is based on adjusting constrained recursive quadratic equations to the hydrant curve of each analyzed fire flow junction. Therefore, it is, in essence, an application of Muller’s method for root-finding. A simple case study is used to illustrate the procedure. Other two real case studies are used to assess the performance of each method. Results show that the proposed method requires, on average, less runs than previous computation methods.