The forces on and responses of a barge-mounted platform (BMP) in waves and currents are investigated using various boundary element methods. A higher-order boundary element method (HOBEM) is developed in the frequency domain using a zero-forward-speed free-surface Green function and the results are compared with an independently developed constant panel method (CPM). The accuracy and convergence rate of the two methods are systematically compared. A time-domain higher-order boundary element method (THOBEM) is also developed to estimate wave forces, hydrodynamic coefficients, wave run-up, and mean drift forces in waves and uniform currents. The zero-current case of THOBEM agrees well with the frequency-domain results. The computed results are compared with experiments. The influence of neighboring boundaries, such as quays, is also studied. The responses of a BMP in the installation site of the South Sea of Korea are presented.