The phenomenon of irregular frequencies is a puzzle in the course of calculating the interaction of waves and structures by the boundary element method. To remove the irregular frequencies, the modified integral domain method is adopted, and continuous higher order elements and partial discontinuous higher order elements are used for discretization. By these means, the effects of the irregular frequencies are effectively removed. Effective strategies have been adopted to deal with singular integrals and nearly singular integrals at different situations. The numerical results of the horizontal wave force on a uniform cylinder in the first order and second order diffraction problems show that the present method has a good validity. At the same time, the influence of collocation parameter on accuracy of numerical results is examined in detail.