Two-dimensional (2-D) formulae for estimating discharge capacity of straight compound channels are reviewed and applied to overbank flows in straight fixed and mobile bed compound channels. The predictive capabilities of these formulae were evaluated using experimental data obtained from the small-scale University of Birmingham channel. Full details of these data and key references may be found at the following www.flowdata.bham.ac.uk (university website). 2-D formulae generally account for bed shear, lateral shear, and secondary flow effects via 3 coefficients f, lambda and Gamma. In this paper, the secondary flow term (Gamma) used within the 2-D methods analysed here is ignored in all applications. Two different 2-D formulae almost give practically the same results for the same data when the secondary flow term is ignored. For overall test cases, the value of dimensionless eddy viscosity lambda used in 2-D formulae was kept at 0.13 as recommended for open channels. 2-D formulae gave good predictions for most of the data sets studied in comparison with the traditional 1-D methods, namely the Single Channel Method (SCM) and the Divided Channel Method (DCM). The accuracy of predictions of 2-D formulae was increased by calibrating of lambda value where the calibration was needed. For overall data, the average errors for each method were Lateral Division Methods (LDMs), with value of 0.13, 2.8%, DCM 14.3% and SCM -26.8%. The average error was 0.5% for LDMs with the calibrated values of lambda.